A projectile of mass is fired so that the horizontal range is . At the highest point the projectile explodes in two parts of masses and respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :
1
16 km
2
1 km
3
10 km
4
2 km
Official Solution
Correct Option: (3)
The correct option is(C): 10 km
Horizontal range is given as
02
PYQ 2014
hard
physicsID: jee-main
A spring of unstretched length has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if it's free end is pulled with uniform velocity is :
1
2
3
4
Official Solution
Correct Option: (4)
03
PYQ 2014
medium
physicsID: jee-main
When a rubber -band is stretched by a distance x, it exerts a restoring force of magnitude , where a and b are constants. The work done in stretching the unstretched rubber-band by is :
1
2
3
4
Official Solution
Correct Option: (3)
04
PYQ 2014
medium
physicsID: jee-main
A bullet looses of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :
1
2
3
Infinite
4
n
Official Solution
Correct Option: (1)
05
PYQ 2016
easy
physicsID: jee-main
Velocity-time graph for a body of mass is shown in figure. Work-done on the body in first two seconds of the motion is :
1
12000 J
2
-12000 J
3
-4500 J
4
-9300 J
Official Solution
Correct Option: (3)
06
PYQ 2016
medium
physicsID: jee-main
A person trying to lose weight by burning at lifts a mass of upto a height of times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies of energy per kg which is converted to mechanical energy with a efficiency rate. Take :
1
2
3
4
Official Solution
Correct Option: (4)
07
PYQ 2016
medium
physicsID: jee-main
A point particle of mass , moves along the uniformly rough track as shown in the figure. The coefficient of friction, between the particle and the rough track equals . The particle is released, from rest, from the point and it comes to rest at a point . The energies, lost by the ball, over the parts, and , of the track, are equal to each other, and no energy is lost when particle changes direction from to . The values of the coefficient of friction and the distance , are, respectively close to :
1
0.2 and 6.5 m
2
0.2 and 3.5 m
3
0.29 and 3.5 m
4
0.29 and 6.5 m
Official Solution
Correct Option: (3)
From work energy theorem and given condition
again
08
PYQ 2016
medium
physicsID: jee-main
A particle of mass is moving in a circle of fixed radius in such a way that its centripetal acceleration at time is given by where is a constant. The power delivered to the particle by the force acting on it, is :
1
2
3
4
Official Solution
Correct Option: (1)
The correct option is(A):
09
PYQ 2017
hard
physicsID: jee-main
Two particles and of equal mass are moving with the same speed as shown in the figure. They collide
completely inelastically and move as a single particle . The angle that the path of makes with the is given by :
1
2
3
4
Official Solution
Correct Option: (1)
10
PYQ 2017
medium
physicsID: jee-main
A body of mass is moving in a medium and experiences a frictional force . Its initial speed is . If, after , its energy is , the value of will be :
1
2
3
4
Official Solution
Correct Option: (3)
11
PYQ 2017
medium
physicsID: jee-main
A time dependent force acts on a particle of mass . If the particle starts from rest, the work done by the force during the first . will be :
1
4.5 J
2
22 J
3
9 J
4
18 J
Official Solution
Correct Option: (1)
12
PYQ 2018
hard
physicsID: jee-main
A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of with respect to each other. The mass of unknown particle is :
1
2
3
4
Official Solution
Correct Option: (2)
In figure (i) before collision, is mass of unknown particle; is mass of proton; is initial velocity.
Now, in figure (ii), is final velocity of unknown particle and is final velocity of proton.
By conservation of momentum, we have Momentum before collision = Momentum after collision Consider -component, we have
Consider -component, we have
Substitute E (2) in E (1), we get
Using Eqs. (2) and (3) in (1), we get
13
PYQ 2018
easy
physicsID: jee-main
A thin rod , free to rotate in the vertical plane about the fixed end , is held horizontal. When the end is released the speed of this end, when the rod makes an angle with the horizontal, will be proportional to : (see figure)
1
2
3
4
Official Solution
Correct Option: (1)
When the end is released and rod makes angle with horizontal, the displacement of centre of mass is Now, we know Here, therefore,
14
PYQ 2018
easy
physicsID: jee-main
A body of mass m starts moving from rest along x-axis so that its velocity varies as where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :
1
2
3
4
Official Solution
Correct Option: (1)
Velocity of the body is given by
Differentiating w.r.t. , we get Acceleration, Force on the body is Distance covered by the body is given by
Work done =Force Distance
15
PYQ 2018
medium
physicsID: jee-main
The mass of a hydrogen molecule is . If hydrogen molecules strike, per second,a fixed wall of area at an angle of to the normal, and rebound elastically with a speed of , then the pressure on the wall is nearly :
1
2
3
4
Official Solution
Correct Option: (1)
16
PYQ 2018
medium
physicsID: jee-main
A particle is moving in a circular path of radius a under the action of an attractive potential . Its total energy is -
1
2
3
zero
4
Official Solution
Correct Option: (3)
[This force provides necessary centripetal force]
Total energy Zero
17
PYQ 2018
medium
physicsID: jee-main
In a collinear collision, a particle with an initial speed strikes a stationary particle of the same mass. If the final total kinetic energy is grater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is -
1
2
3
4
Official Solution
Correct Option: (2)
It is a case of superelastic collision
18
PYQ 2019
medium
physicsID: jee-main
A force acts on a object so that its position is given as a function of time as . What is the work done by this force in first seconds ?
1
850 J
2
900 J
3
950 J
4
875 J
Official Solution
Correct Option: (2)
at
W.D. = KE W.D.
19
PYQ 2019
medium
physicsID: jee-main
A man (mass = ) and his son (mass = ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of with respect to the man. The speed of the man with respect to the surface is :
1
2
3
4
Official Solution
Correct Option: (1)
and
20
PYQ 2019
medium
physicsID: jee-main
A block of mass , lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant . The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force , the maximum speed of the block is :
1
2
3
4
Official Solution
Correct Option: (3)
Maximum speed is at mean position (equilibrium).
21
PYQ 2019
medium
physicsID: jee-main
A uniform cable of mass and length is placed on a horizontal surface such that its part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :
1
2
3
4
Official Solution
Correct Option: (2)
Mass of the hanging part =
work done W = mgh Option (2)
22
PYQ 2019
medium
physicsID: jee-main
An alpha-particle of mass m suffers 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, of its initial kinetic energy. The mass of the nucleus is :
1
4 m
2
3.5 m
3
2 m
4
1.5 m
Official Solution
Correct Option: (1)
23
PYQ 2019
easy
physicsID: jee-main
A spring whose unstretched length is has a force constant . The spring is cut into two pieces of unstretched lengths and where, = and is an integer. The ratio of the corresponding force constants, and will be :
1
2
3
4
Official Solution
Correct Option: (3)
24
PYQ 2019
hard
physicsID: jee-main
A piece of wood of mass is dropped from the top of a height building. At the same time, a bullet of mass is fired vertically upward, with a velocity , from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is :
1
30 m
2
10 m
3
40 m
4
20 m
Official Solution
Correct Option: (3)
Time taken for the particles to collide,
Speed of wood just before collision = & speed of bullet just before collision = Now, conservation of linear momentum just before and after the collision -
Max. height reached by body
Height above tower =
25
PYQ 2020
hard
physicsID: jee-main
Two particles of equal mass m have respective initial velocities and They collide completely inelastically. The energy lost in the process is :
1
2
3
4
Official Solution
Correct Option: (4)
From momentum conservation
Final kinetic energy Initial kinetic energy
Loss in
26
PYQ 2020
medium
physicsID: jee-main
A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :
1
2
3
4
Official Solution
Correct Option: (3)
27
PYQ 2020
easy
physicsID: jee-main
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : ( )
1
2
3
4
Official Solution
Correct Option: (4)
28
PYQ 2021
medium
physicsID: jee-main
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :
1
t³/2
2
t¹/2
3
t²/3
4
t
Official Solution
Correct Option: (1)
Step 1: Power .
Step 2: .
Step 3: .
Therefore, .
29
PYQ 2021
medium
physicsID: jee-main
A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is _________. (Take )
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
This problem can be solved using the principle of conservation of mechanical energy. Since the table is smooth, there is no friction, and the loss in potential energy of the chain as it slips off equals the gain in its kinetic energy. Step 2: Key Formula or Approach:
1. Potential Energy of a part of the chain: , where is the depth of the center of mass of the hanging part from the table level.
2. Conservation of Energy: . Since it starts from rest, , so . Step 3: Detailed Explanation:
Given: Total length , Total mass .
Mass per unit length .
Initial State:
Length on table = 2 m, Hanging length .
Mass of hanging part .
Center of mass of the hanging part is at a distance below the table.
Initial Potential Energy .
Final State:
The entire chain has slipped off. Hanging length .
Total mass hanging .
Center of mass of the chain is now at below the table.
Final Potential Energy .
Calculating Kinetic Energy (k):
By conservation of energy:
Step 4: Final Answer:
The value of is 40.
30
PYQ 2021
medium
physicsID: jee-main
Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angles 45 and 60 with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is . The value of x is ________.
Official Solution
Correct Option: (1)
Step 1: Understanding the Question:
Two forces do the same amount of work over the same distance, but they act at different angles. We need to find the ratio of the magnitudes of these forces. Step 2: Key Formula or Approach:
The work done ( ) by a constant force ( ) that makes an angle with the displacement ( ) is given by:
We are given that the work done by person A ( ) is equal to the work done by person B ( ). Step 3: Detailed Explanation:
Let be the force applied by person A at an angle .
Let be the force applied by person B at an angle .
The displacement is for both. Work done by A:
Work done by B:
Given :
The displacement cancels out:
We need to find the ratio .
Now, substitute the values of the trigonometric functions:
So, the ratio is:
The problem states that this ratio is equal to .
By comparing the two sides, we can see that:
Step 4: Final Answer:
The value of x is 2.
31
PYQ 2021
medium
physicsID: jee-main
Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ________ .
Official Solution
Correct Option: (1)
The relationship between kinetic energy (KE) and linear momentum (p) is given by . This can be rearranged to express momentum as . Let the two particles be particle 1 and particle 2, with masses g and g. We are given that their kinetic energies are equal: . Let's find the ratio of their momenta, : . Since , the equation simplifies to: . Substituting the given masses: . The ratio of their linear momenta is 1 : 2. The problem states that the ratio is n : 2. By comparing the two ratios, we find that n = 1.
32
PYQ 2021
medium
physicsID: jee-main
A block moving horizontally on a smooth surface with a speed of splits into two equal parts. If one of the parts moves at in the same direction, then the fractional change in the kinetic energy will be where .
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept: This problem involves the conservation of linear momentum and the calculation of kinetic energy before and after the explosion (splitting) of the block. Step 2: Key Formula or Approach: 1. Conservation of Momentum: . 2. Kinetic Energy: . 3. Fractional Change: . Step 3: Detailed Explanation: Let the total mass be . The block splits into two equal parts, so each mass is . 1. Initial State: - Initial speed . - Initial Momentum: . - Initial Kinetic Energy: . 2. Final State: - Mass 1 ( ) moves at . - Mass 2 ( ) moves at speed . - By Momentum Conservation: .
- Final Kinetic Energy:
3. Fractional Change: - Change in KE: . - Fractional Change: . Comparing with , we get . Step 4: Final Answer: The value of x is 1.
33
PYQ 2021
medium
physicsID: jee-main
The potential energy (U) of a diatomic molecule is . The equilibrium distance between two atoms will be , where a = _________.
Official Solution
Correct Option: (1)
Step 1: At equilibrium, the force .
Step 2: .
Step 3: .
Step 4: .
Step 5: .
Step 6: Comparing with , we get (and ).
34
PYQ 2021
medium
physicsID: jee-main
A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of to the vertical will be ( ) ________ m/s.
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept: The motion of a pendulum is governed by the Law of Conservation of Mechanical Energy. As the bob rises, kinetic energy is converted into potential energy. Step 2: Key Formula or Approach: 1. Potential energy gain: . 2. Energy conservation: . Step 3: Detailed Explanation: Given: , , . Calculate the vertical height :
Using conservation of energy:
Step 4: Final Answer: The speed of the bob at is 2 m/s.
35
PYQ 2021
medium
physicsID: jee-main
As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s²) The value of 'x' to the nearest integer is __________. [Note: Usually m and m in this problem]
Official Solution
Correct Option: (1)
Step 1: Use Law of Conservation of Energy: .
Step 2: . If :
Step 3: .
36
PYQ 2021
medium
physicsID: jee-main
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:
1
2
3
4
Official Solution
Correct Option: (3)
When an engine supplies constant power P, this power is used to increase the kinetic energy of the automobile.
Power , where K is the kinetic energy. Since the automobile starts from rest, its kinetic energy at any time t is .
. Since P is constant, we can integrate with respect to time to find the kinetic energy:
. From this, we can find the velocity v as a function of time.
. Position x is the integral of velocity v with respect to time. Since it starts from the origin, .
. . . To match the format of the options, we bring the constant inside the square root.
. . This can be written as .
37
PYQ 2021
medium
physicsID: jee-main
A small block slides down from the top of hemisphere of radius R=3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is ________ m. (Assume there is no friction between the block and the hemisphere)
Official Solution
Correct Option: (1)
Let the block of mass 'm' lose contact at a point A, which is at a vertical height 'h' from the top.
Let be the angle that the radius to point A makes with the vertical. The vertical distance dropped is . At point A, the forces acting on the block are the normal force (N) and gravity (mg). The component of gravity towards the center of the hemisphere is .
The net force towards the center provides the centripetal force:
. The block loses contact when the normal force N becomes zero.
At , we have , which simplifies to . (Equation 1) Now, apply the principle of conservation of mechanical energy between the top of the hemisphere (initial position) and point A (final position).
Initial Energy (at top): (taking the base of the hemisphere as the reference level).
Final Energy (at A): . Equating initial and final energies:
.
.
. (Equation 2) Now, equate the two expressions for from Equation 1 and Equation 2.
.
.
. The height 'h' at which the block loses contact is the vertical distance it has dropped.
. Given the radius R = 3 m:
m.
38
PYQ 2021
medium
physicsID: jee-main
Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that J, the incorrect statement for this system is : [ where K.E. = kinetic energy ]
1
at , K.E. is greatest and the particle is moving at the fastest speed.
2
at , K.E. is smallest and the particle is moving at the slowest speed.
3
at , K.E. is constant throughout the region.
4
at , K.E. = 4 J.
Official Solution
Correct Option: (2)
The total mechanical energy of the system is constant, .
The kinetic energy is given by .
Since K.E. must be non-negative ( ), the particle can only exist in regions where . Let's analyze each statement:
(A) At , the potential energy is at its minimum value (close to 0 J from the graph).
Therefore, will be maximum. Since , maximum K.E. implies the fastest speed. This statement is correct. (C) For the region , the graph shows that the potential energy is constant at a value of 6 J.
So, . Since U(x) is constant, K.E. is also constant. This statement is correct. (D) At , the graph shows the potential energy is 4 J.
So, . This statement is correct. (B) For the region , the graph shows that the potential energy is constant at 8 J. According to the principle of conservation of energy, a particle with total energy J can only access regions where J.
The region has J, so K.E. would be . The particle can reach the point (this is a turning point), but it cannot enter the region . This region is classically forbidden for the particle. Therefore, any statement describing the particle's motion "at " is fundamentally incorrect because the particle cannot be there.
39
PYQ 2021
medium
physicsID: jee-main
A ball of mass 4 kg, moving with a velocity of 10 ms , collides with a spring of length 8 m and force constant 100 Nm . The length of the compressed spring is x m. The value of x, to the nearest integer, is __________.
Official Solution
Correct Option: (1)
Step 1: Use Conservation of Mechanical Energy. The kinetic energy of the ball is converted into elastic potential energy of the spring at maximum compression.
Step 2: Solve for compression ( ).
Step 3: Find the final length of the spring ( ).
40
PYQ 2021
medium
physicsID: jee-main
Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be A/1, so the value of A will be ______
Official Solution
Correct Option: (1)
Step 1: The relationship between Kinetic Energy ( ) and Momentum ( ) is given by .
Step 2: Since momentum is equal for both, .
Step 3: Therefore, .
Comparing this to , we find .
41
PYQ 2022
hard
physicsID: jee-main
Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms–2. The value of F is (Take g = 10 ms–2)
1
3360 N
2
3380 N
3
3120 N
4
3240 N
Official Solution
Correct Option: (3)
In frame of block of mass M moving with acceleration a.
m1a – T = 2m1 10a – T = 20 …(i)
T – m2g = 2m2 T – 200 = 40 T = 240 …(ii) From equation 1 and 2 10a = 260 or, a = 26 m/s2 for block F = (M + m2)a F= 120 × 26 F= 3120 N
So, the correct option is (C): 3120 N
42
PYQ 2022
medium
physicsID: jee-main
Three masses and are arranged in a system as shown in figure All the surfaces are frictionless and strings are inextensible and weightless The pulleys are also weightless and frictionless A force is applied on the system so that the mass moves upward with an acceleration of The value of is : (Take )
1
3360 N
2
3380 N
3
3120 N
4
3240 N
Official Solution
Correct Option: (1)
The value of F is 3360 N. Therefore, the correct option is (A): 3360 N
43
PYQ 2022
hard
physicsID: jee-main
A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N.If the maximum speed with which the stone can revolve is k/\pi rev./min.The value of K is(Assume the string is massless and unstretchable)
1
400
2
300
3
600
4
800
Official Solution
Correct Option: (3)
T= ⇒80=0.1×(2π× × )2×2 ⇒ = ⇒K = 30 × 20 = 600 The correct option is (C) : 600
44
PYQ 2022
medium
physicsID: jee-main
As per the given figure, two blocks each of mass are connected to a spring of spring constant . If both are given velocity v in opposite directions, then maximum elongation of the spring is:
1
2
3
4
Official Solution
Correct Option: (2)
∵ Loss in Kinetic Energy = Gain in spring energy
So, the correct option is (B):
45
PYQ 2022
medium
physicsID: jee-main
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as
1
Zero
2
mk2r2t2
3
mk2r2t
4
mk2rt
Official Solution
Correct Option: (3)
The correct answer is (C) : mk2r2t
or and
= power delivered
46
PYQ 2022
medium
physicsID: jee-main
A ball is projected vertically upward with an initial velocity of 50 ms–1 at t = 0 s. At t = 2 s, another ball is projected vertically upward with same velocity. At t = _____s, second ball will meet the first ball. (g = 10 ms–2)
Official Solution
Correct Option: (1)
The correct answer is : (6) At t = 2 s, v1 = 50 – 2 × 10 = 30 m/s v2 = v2 ∴ arel = g – g = 0
Therefore, Required time t = 2 + 4 = 6 s
47
PYQ 2022
medium
physicsID: jee-main
Water falls from a 40 m high dam at the rate of 9 \times 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is : (Take g = 10 ms–2)
1
25
2
50
3
100
4
18
Official Solution
Correct Option: (2)
To determine the number of 100 W lamps that can be lit using the hydroelectric energy generated, we need to follow these steps:
Calculate the gravitational potential energy:
Given the height , mass flow rate , and acceleration due to gravity .
Convert the mass flow rate to kg/s: .
The gravitational potential energy per second is given by: .
Calculate the electrical energy output:
Only 50% of the gravitational potential energy is converted to electrical energy, so .
Determine the number of 100 W lamps:
Since power is energy per unit time, and power is measured in watts (1 J/s = 1 W), the electrical power available is .
Each lamp requires , so the number of lamps that can be lit is: .
Thus, the number of 100 W lamps that can be lit is 50.
48
PYQ 2022
medium
physicsID: jee-main
A block of mass M placed inside a box descends vertically with acceleration ‘a’.The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ‘a’ will be
1
2
3
4
Official Solution
Correct Option: (3)
The correct answer is (C) : By Using Newton’s 2nd law , we get
49
PYQ 2022
medium
physicsID: jee-main
In the given figure, the block of mass m is dropped from the point ‘A’. The expression for kinetic energy of block when it reaches point ‘B’ is
Fig.
1
2
3
mg(y - y0)
4
mgy0
Official Solution
Correct Option: (4)
To determine the kinetic energy of the block when it reaches point ‘B’, we can use the principle of conservation of energy. Initially, at point ‘A’, the block has potential energy but no kinetic energy. As it falls to point ‘B’, this potential energy is converted into kinetic energy.
Step 1: Calculate Initial Potential Energy at Point ‘A’
The potential energy at height is given by:
PE = mgy_0
where:
m is the mass of the block
g is the acceleration due to gravity
y_0 is the initial height
Step 2: Consider Energy Conservation
When the block reaches point ‘B’, its potential energy is zero (assuming the height of point ‘B’ is zero). According to the conservation of energy, the initial potential energy is converted entirely into kinetic energy at point ‘B’.
Step 3: Determine Kinetic Energy at Point ‘B’
The kinetic energy at point ‘B’ is equal to the initial potential energy:
KE = mgy_0
This implies the kinetic energy of the block when it reaches point ‘B’ is .
Conclusion:
The correct expression for the kinetic energy of the block at point ‘B’ is mgy0. This corresponds to option 4.
Fig.
50
PYQ 2023
easy
physicsID: jee-main
Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statement, choose the correct answer from the options given below:
Official Solution
Correct Option: (1)
51
PYQ 2023
easy
physicsID: jee-main
Assertion A: If and represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: Reason R: First law of thermodynamics is based on the law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:
Official Solution
Correct Option: (1)
52
PYQ 2023
medium
physicsID: jee-main
Statement (1): A truck and a car moving with equal kinetic energy are stopped by equal retarding force. Both will cover equal distance to stop. Statement (2): A car moving towards east suddenly changes its direction towards north with same speed. Its acceleration is zero. In the light of given statements, choose the most appropriate answer from the options given below.
1
Both (1) and (2) are true
2
Both (1) and (2) are false
3
(1) is true, (2) is false
4
(1) is false, (2) is true
Official Solution
Correct Option: (3)
53
PYQ 2023
hard
physicsID: jee-main
A small particle moves to position from its initial position under the action of force . The value of work done will be ________
Official Solution
Correct Option: (1)
So, The correct answer is 40.
54
PYQ 2023
easy
physicsID: jee-main
A spherical body of mass starting from rest acquires a kinetic energy of at the end of second The force acted on the body is ___
Official Solution
Correct Option: (1)
The kinetic energy is related to velocity as:
Substitute the given values ( ):
The acceleration is found using:
Since the body starts from rest ( ) and reaches in :
The force acting on the body is:
55
PYQ 2023
medium
physicsID: jee-main
Vectors and are perpendicular to each other when , the ratio of to is The value of is __
Official Solution
Correct Option: (1)
For two vectors to be perpendicular, their dot product must be zero:
Substitute and :
Simplify:
This gives the first equation:
From the problem, another equation is given:
Solve the simultaneous equations:
Multiply equation (1) by 2:
Multiply equation (2) by 3:
Add equations (3) and (4):
Substitute into equation (2):
The ratio of to is:
Thus:
56
PYQ 2023
medium
physicsID: jee-main
In the circuit shown in the figure, the ratio of the quality factor and the band width is__s
Official Solution
Correct Option: (1)
The relations for an LCR circuit are: The resonant angular frequency is given by: Simplify: The ratio is: Substituting the values: Simplify further: Thus, the ratio of the quality factor to the bandwidth is:
57
PYQ 2023
hard
physicsID: jee-main
A bag of sand of mass is suspended by a rope A bullet of travelling with speed gets embedded in it, then loss of kinetic energy will be
1
2
3
4
Official Solution
Correct Option: (2)
Pi=Pf ( no any external force ) 0.2×10=10×v v=0.2m/sec
Loss in K.E. =21×(0.2)×102−21×10(0.2)2 =21×10×(0.2)[10−0.2] =9.8J
58
PYQ 2023
medium
physicsID: jee-main
A stone of mass is tied to end of a massless string of length If the breaking tension of the string is , then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :
1
2
3
4
Official Solution
Correct Option: (2)
The correct answer is (B) :
59
PYQ 2023
easy
physicsID: jee-main
Heat is given to an ideal gas in an isothermal process A Internal energy of the gas will decrease B Internal energy of the gas will increase C Internal energy of the gas will not change D The gas will do positive work E The gas will do negative work Choose the correct answer from the options given below:
A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30◦ with horizontal with an affective acceleration of 1 ms−2. The power delivered by the pulling force at t = 10 s from the starts is W. [use g=10 ms−2] (Calculate the nearest integer value)
Official Solution
Correct Option: (1)
Given:
Mass ( ) =
Angle of incline ( ) =
Acceleration ( ) =
Time ( ) =
Gravitational acceleration ( ) =
Initial velocity ( ) =
Step 1: Resolve Forces and Find Pulling Force ( )
The forces acting along the incline include:
Pulling force ( ) acting upwards along the incline.
The component of weight ( ) acting downwards along the incline.
The force causing acceleration ( ) acting upwards.
Applying Newton’s second law along the incline:
Substitute the given values ( ):
Simplify:
Step 2: Calculate the Final Velocity ( )
Using the first equation of motion:
Substitute :
Step 3: Calculate the Power ( )
Power is the rate at which work is done, given by:
Substitute and :
Final Answer:
The power delivered by the pulling force is .
61
PYQ 2023
medium
physicsID: jee-main
A body of mass is moving with a momentum of . Now a force of acts on the body in the direction of its motion for . The increase in the kinetic energy of the body is _____ J.
Official Solution
Correct Option: (1)
The kinetic energy of a body is given by: where: is the momentum, is the mass of the body. Step 1: Initial kinetic energy. The initial momentum is . The initial kinetic energy is: Step 2: Final kinetic energy. The force acts for , producing an additional momentum: The final momentum is: The final kinetic energy is: Step 3: Increase in kinetic energy. The increase in kinetic energy is: Final Answer: The increase in kinetic energy is:
62
PYQ 2023
medium
physicsID: jee-main
A body of mass begins to move under the action of a time-dependent force where and are unit vectors along and axes. The power developed by the above force, at the time , will be _____ W.
Official Solution
Correct Option: (1)
The force acting on the body is:
The acceleration is given by Newton’s second law:
The velocity is obtained by integrating acceleration:
At :
The power is given by:
Substitute and :
Thus, the power at is .
63
PYQ 2023
medium
physicsID: jee-main
Force acting on a particle moving along the x - axis is given by F = (2 + 3x)i. The work done by this force from x = 0 to x = 4 m is
1
16J
2
32J
3
4J
4
8J
Official Solution
Correct Option: (2)
The correct option is (B): 32J
64
PYQ 2023
easy
physicsID: jee-main
A ball is dropped from a height of If the coefficient of restitution for the collision between ball and floor is , after hitting the floor, the ball rebounds to a height of ___
Official Solution
Correct Option: (1)
The height to which the ball rebounds is given by:
where is the coefficient of restitution and is the initial height. Substituting the values:
65
PYQ 2023
medium
physicsID: jee-main
Two bodies having the same linear momentum have a ratio of kinetic energy as 16:9. Find the ratio of masses of these bodies.
1
2
3
4
Official Solution
Correct Option: (1)
Let the masses of the two bodies be and , and their velocities be and respectively.
Given:
Step 1: Express Kinetic Energies
Step 2: Use Momentum Equality
Step 3: Substitute in the Kinetic Energy Ratio
Step 4: Determine the Ratio of Masses
Hence, the correct ratio of their masses is .
66
PYQ 2023
easy
physicsID: jee-main
A body of mass collides head on elastically with a stationary body of mass After collision, the smaller body reverses its direction of motion and moves with a speed of The initial speed of the smaller body before collision is ___
Official Solution
Correct Option: (1)
The correct answer is 4.
67
PYQ 2023
hard
physicsID: jee-main
A variable force acts on a body moving along x-axis. Find the work done by this force in displacing the body from m to m. (K is constant)
1
2
3
4
Official Solution
Correct Option: (2)
When force remains constant and motion occurs along a straight path, work is calculated as the product of force and distance traveled. However, when force varies within the distance traveled, calculus aids in resolving the problem by breaking it down into infinitesimal steps where force can be considered constant. Consequently, the work accomplished by a variable force is expressed as,
Here, the force is described by N, and the displacement ranges from m to m. Now the work performed,
So, the correct option is (B):
68
PYQ 2023
hard
physicsID: jee-main
A body of mass travels on straight line path with velocity The net workdone by the force during its displacement from to is :
1
64 J
2
60 J
3
120 J
4
128 J
Official Solution
Correct Option: (2)
The correct option is (B) : 60 J vi = 3(0)2 + 4 = 4 ≅ x = 0 vF = 3(2)2 + 4 = 16 ≅ x = 2
69
PYQ 2023
medium
physicsID: jee-main
Mass of body = 500 kg, μ= 0.7. Find work required to move a distance of 4 Km if the body moves with velocity 10 m/s.
1
3.5 × 106 J
2
28 × 106 J
3
7 × 106 J
4
14 × 106 J
Official Solution
Correct Option: (4)
Since v = const. ⇒ F = μmg = 0.7 × 500 × 10 = 3500 N W = FS = 3.5 × 103 × 4 × 103 = 14 × 106 J
70
PYQ 2023
medium
physicsID: jee-main
In an experiment with Vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and 6th division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm and 3.3 cm marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as
1
3.26 cm
2
3.25 cm
3
3.22 cm
4
3.18 cm
Official Solution
Correct Option: (4)
Step 1: Calculating the zero error and the actual measurement. The zero error in the vernier scale is:
Now, the diameter measured with the help of the Vernier scale is:
The actual diameter is:
71
PYQ 2023
hard
physicsID: jee-main
The variation of stopping potential (V0) as a function of the frequency (v) of the incident light for a metal is shown in figure. The work function of the surface is
1
1.36 eV
2
2.98 eV
3
2.07 eV
4
18.6 eV
Official Solution
Correct Option: (3)
Step 1: Understanding the photoelectric equation. In the photoelectric effect, the stopping potential ( ) is related to the frequency ( ) of the incident light by the equation:
Where: is the stopping potential (in volts). is the frequency of the incident light (in Hz). is the threshold frequency (below which no photoelectric emission occurs). is the charge of the electron ( ). is Planck's constant ( ). Step 2: Identifying the threshold frequency. From the graph, we can observe that the stopping potential becomes non-zero at a frequency of approximately . This is the threshold frequency . Step 3: Calculating the work function.
At the threshold frequency, the stopping potential is zero. We use the equation:
Substituting the values:
To convert this to eV, divide by the charge of the electron:
Thus, the work function is .
72
PYQ 2023
medium
physicsID: jee-main
A force acts on a particle in the -direction where is in newton and is in meter. The work done by this force during a displacement from to is _____ J.
Official Solution
Correct Option: (1)
The work done by a force is given by the integral: Where . Substituting into the integral: Solving this: Thus, the work done is 32 J.
73
PYQ 2023
medium
physicsID: jee-main
A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is J. The value of n will be ____________
Official Solution
Correct Option: (1)
74
PYQ 2023
hard
physicsID: jee-main
In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. j/s represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of will be ______.
Official Solution
Correct Option: (1)
Step 1: Power Supplied by the Battery
The power supplied by the battery is given by:
where is the emf of the battery and is the resistance. Substituting :
Step 2: Power Stored in the Inductor
The maximum power stored in the inductor is given as:
Step 3: Relating and
Since the total resistance is , and the stored energy in the inductor is proportional to the power supplied:
Simplify:
Step 4: Find the Ratio
Since (from standard proportionality), the ratio is:
75
PYQ 2023
hard
physicsID: jee-main
Identify the correct statements from the following: A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity in zero. E. Work done by the air resistance on an oscillating pendulum in negative. Choose the correct answer from the options given below:
1
B, D and E only
2
A and C Only
3
𝐵 and 𝐷 only
4
𝐵 and 𝐸 only
Official Solution
Correct Option: (4)
- (B) Work done by gravity is negative because the gravitational force opposes the upward motion. - (E) Work done by air resistance is always negative because it opposes motion. - Other statements are incorrect because: - (A) Work done by a man is positive as the applied force is in the direction of displacement. - (C) Work done by friction is negative, not positive. - (D) Work done is zero only if there is no displacement, not due to roughness.
76
PYQ 2023
medium
physicsID: jee-main
Dimension of should be equal to
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Use the relationship between µ0, ϵ0, and the speed of light.- Given , we know:
.
Step 2: Analyze the dimensions.- Dimensional formula for c: [c] = .- Hence, = = .
Final Answer: The dimension is
77
PYQ 2023
medium
physicsID: jee-main
The amplitude of 15sin(1000πt) is modulated by 10sin(4πt) signal. The amplitude modulated signal contains frequency (ies) of (A) 500 Hz (B) 2 Hz (C) 250 Hz (D) 498 Hz (E) 502 Hz Choose the correct answer from the options given below:
1
A, D and E only
2
A and B only
3
A and B only
4
A and D only
Official Solution
Correct Option: (1)
The correct option is(A): A, D and E only
78
PYQ 2023
medium
physicsID: jee-main
An engine operating between the boiling and freezing points of water will have 1. efficiency more than 27% 2. efficiency less than the efficiency a Carnot engine operating between the same two temperatures. 3. efficiency equal to 27% 4. efficiency less than 27%
1
B and C only
2
B and D only
3
A and B only
4
B, C and D only
Official Solution
Correct Option: (2)
The correct option is(B): B and D only
79
PYQ 2023
easy
physicsID: jee-main
For the following circuit and given inputs A and B, choose the correct option for output 'Y'
1
2
3
4
Official Solution
Correct Option: (3)
The correct option is: (C):
80
PYQ 2023
medium
physicsID: jee-main
The amplitude of 15sin(1000πt) is modulated by 10sin(4πt) signal. The amplitude modulated signal contains frequency(ies) of (A) 500 Hz (B) 2 Hz (C) 250 Hz (D) 498 Hz (E) 502 Hz Choose the correct answer from the options given below:
1
A, D and E only
2
A and B only
3
A and C only
4
A and D only
Official Solution
Correct Option: (1)
Solution: Carrier signal: Modulating signal:
The general form of a sinusoidal wave is , where is the amplitude, is the frequency, and is time.
The frequencies present in the amplitude modulated signal are:
500 Hz (1)
498 Hz (4)
502 Hz (5)
Therefore, the correct answer is (4) (1), (4) and (5) only.
81
PYQ 2023
medium
physicsID: jee-main
A common example of alpha decay is
Official Solution
Correct Option: (1)
Energy released is given by the equation:
Here, the mass defect is:
Thus,
Therefore, the energy released during the alpha decay of is 4.0986 MeV.
82
PYQ 2024
hard
physicsID: jee-main
A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:
1
1:1
2
2:1
3
4
1:2
Official Solution
Correct Option: (3)
The work done by gravity is independent of the path taken. It depends only on the change in vertical displacement. Therefore, in both cases (pulled straight up and along the ramp), the work done remains the same as the vertical displacement is the same.
83
PYQ 2024
easy
physicsID: jee-main
A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :
1
2
3
4
Official Solution
Correct Option: (2)
To solve this problem, we need to calculate the maximum compression in the spring when the block hits it. We'll use energy conservation principles, factoring in gravitational potential energy, work done by friction, and spring potential energy.
Initially, the block is released from rest, meaning its initial kinetic energy is zero. It starts with gravitational potential energy at the incline's top, given by: , where , (assuming near the Earth's surface), and .
Calculate the height:
Substitute into the potential energy formula:
The block slides down the incline and across a rough surface (friction coefficient ) for . Calculate the work done by friction:
By energy conservation, the gravitational potential energy is converted into spring potential energy and work done against friction:
Substitute the known values:
Solve for :
First, simplify the equation:
Re-arrange to solve for :
Divide both sides by 50:
Solve for :
Therefore, the maximum compression in the spring when the block hits the spring is .
84
PYQ 2024
medium
physicsID: jee-main
A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:
1
150 N
2
3 N
3
30 N
4
300 N
Official Solution
Correct Option: (3)
To calculate the force exerted by the cricket ball on the hand of the player, we can use the impulse-momentum theorem. The theorem states that the impulse experienced by an object is equal to the change in its momentum. Mathematically, this can be expressed as:
Where:
is the force exerted.
is the time over which the force is applied.
is the change in momentum.
First, compute the initial and final momentum:
The initial momentum , where (mass of the ball converted to kg) and . Thus, .
The final momentum since the ball is caught and brought to rest.
The change in momentum .
Considering only the magnitude (ignore the negative sign), the impulse is equal to .
Now, calculate the force using the formula:
Substitute the values:
Therefore, the magnitude of the force exerted by the ball on the hand of the player is 30 N.
85
PYQ 2026
easy
physicsID: jee-main
A ball of mass 100 g is projected with velocity 20 m/s at with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:
1
5 J
2
15 J
3
20 J
4
zero
Official Solution
Correct Option: (2)
Concept: In projectile motion: The horizontal component of velocity remains constant. The vertical component of velocity becomes zero at the highest point Decrease in kinetic energy from projection to highest point is equal to the loss of kinetic energy associated with the vertical component of velocity. Step 1: Given data: Step 2: Vertical component of velocity: Step 3: Kinetic energy associated with vertical motion:
86
PYQ 2026
easy
physicsID: jee-main
A curve is given between the potential energy of a particle and its position on the -axis as shown.
Given:If is the force acting on the particle during motion from to ,
similarly , and are the forces during to ,
to and to respectively, arrange the magnitudes of these forces
in decreasing order.
1
2
3
4
Official Solution
Correct Option: (2)
Force acting on a particle is related to the potential energy by:
Hence, the magnitude of force is equal to the magnitude of the slope of the -- graph. On segment : slope On segment : slope On segment : slope On segment : slope Arranging in decreasing order of magnitude:
87
PYQ 2026
medium
physicsID: jee-main
Given below are two statements: Statement I: An object moves from position to position under a conservative force field . The work done by the force is Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below:
1
Statement I is true but Statement II is false
2
Statement I is false but Statement II is true
3
Both Statement I and Statement II are true
4
Both Statement I and Statement II are false
Official Solution
Correct Option: (1)
Step 1: Analyze Statement I. For a conservative force field, the work done in moving a particle from position to is equal to the negative change in potential energy. Mathematically,
This expression correctly represents the work done by a conservative force. Hence, Statement I is true.
Step 2: Analyze Statement II. Although a particle can move between two points along infinitely many paths, the defining property of a conservative force is that the work done depends only on the initial and final positions and not on the path followed. Therefore, the work done by a conservative force does not change with the path. Hence, Statement II is false.
Step 3: Final conclusion. Statement I is true but Statement II is false.
Final Answer:
88
PYQ 2026
easy
physicsID: jee-main
A large drum having radius is spinning around its axis with angular velocity , as shown in figure. The minimum value of so that a body of mass remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass as , is :
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept: For the mass to remain stuck to the vertical wall, the upward frictional force must balance the weight of the mass. The normal force required for friction is provided by the centripetal acceleration due to the drum's rotation.
Step 2: Key Formula or Approach: 1. Weight (downwards). 2. Normal force (towards center). 3. Static friction .
Step 3: Detailed Explanation: For vertical equilibrium:
Since , we have:
Cancelling from both sides:
The minimum angular velocity is:
Step 4: Final Answer: The minimum angular velocity is .
89
PYQ 2026
medium
physicsID: jee-main
Two masses and are connected by a light string going over a pulley (disc) of mass with radius . The pulley is mounted in a vertical plane and is free to rotate about its axis. The mass is released from rest and its speed when it has descended through a height of is ____________ m/s. (Assume string does not slip and ).
Official Solution
Correct Option: (1)
Step 1: Use conservation of energy. Loss in gravitational potential energy of the system
Step 2: Write kinetic energy of the system. Kinetic energy consists of translational KE of both masses and rotational KE of the pulley. For a disc, Since no slipping,
Step 3: Apply energy conservation. Considering descent of block and full system dynamics, the final speed is
Final Answer:
90
PYQ 2026
easy
physicsID: jee-main
Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding the Question:
The question asks us to rank the magnitudes of the force in different regions (AB, BC, CD, DE) based on a given potential energy (V) versus position (x) graph. Step 2: Key Formula or Approach:
The relationship between force (F) and potential energy (V) is given by the negative gradient of the potential energy. For one dimension, this is:
The magnitude of the force is the absolute value of the slope of the V-x graph:
We need to calculate the magnitude of the slope for each region. Step 3: Detailed Explanation:
From the graph, we can determine the coordinates of the points:
A = (0, 0), B = (1, 1), C = (2, 3), D = (4, 3), E = (6, 1). Now, we calculate the slope for each region:
\begin{itemize} \item Region AB: The slope is . Therefore, the magnitude of the force is . \item Region BC: The slope is . Therefore, the magnitude of the force is . \item Region CD: The slope is . Therefore, the magnitude of the force is . \item Region DE: The slope is . Therefore, the magnitude of the force is .
\end{itemize} Step 4: Final Answer:
Ranking the magnitudes of the forces from high to low:
So, the ranking is .
Looking at the options, option (C) fits this ranking.
91
PYQ 2026
medium
physicsID: jee-main
A curve is given between potential energy of a particle and its position on the x-axis. Given:
If be the force acting on the particle during to , similarly are the forces during to , to , and to respectively. Arrange magnitudes of these forces in decreasing order.
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Force is the negative derivative of potential energy. The force acting on the particle is given by . Step 2: Understanding the graph. From the given graph, the slope of the potential energy curve gives the magnitude of the force. The steeper the slope, the greater the force. Step 3: Compare slopes. The slope of the potential energy curve is greatest between to , followed by to , then to , and the least between to . Therefore, the order of forces is: Step 4: Conclusion. The correct answer is option (2).
92
PYQ 2026
medium
physicsID: jee-main
A body of mass 4 kg is placed on a plane at a point P having coordinate m. Under the action of force N, it moves to a new point Q having coordinates m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:
1
2
3
4
Official Solution
Correct Option: (1)
Concept:
Average power Instantaneous power Work done by a constant force Step 1: Displacement of the body:
Step 2: Work done by the force:
Step 3: Average power:
Step 4: Acceleration of the body:
Step 5: Velocity at the end of 4 sec (initial velocity zero):
Step 6: Instantaneous power at sec:
Step 7: Required ratio:
93
PYQ 2026
easy
physicsID: jee-main
Position of the particle of mass 2 kg varies as function of time as . Find out work done on the particle from sec to sec.
1
18 joule
2
30 joule
3
34 joule
4
24 joule
Official Solution
Correct Option: (4)
Step 1: Understand the formula for work done. The work done on a particle is given by the change in kinetic energy:
where is the mass of the particle, and and are the initial and final velocities of the particle. Step 2: Find the velocity of the particle. The position of the particle is given by:
To find the velocity, we differentiate with respect to time :
Step 3: Calculate the velocities at sec and sec. At sec:
At sec:
Step 4: Calculate the work done. The mass of the particle is given as . Using the work-energy theorem:
Thus, the work done on the particle is 24 joules.
