The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in and (ii) the time at which the car will catch up with the scooter are, respectively.
1
112.5 m and 22.5 s
2
337.5 m and 25 s
3
112.5 m and 15 s
4
225.5 m and 10 s
Official Solution
Correct Option: (1)
From the given velocity-time graph we observe that the car is having uniformly accelerated motion while the scooter is having uniform motion, thus, displacement of car is given as where is the initial velocity and is the time and is acceleration.
Now we know initial velocity is zero Therefore, ...(1)
Given and acceleration Therefore, Now displacement of scooter is given as From graph, we get , therefore, Thus, the difference between the distance travelled by car and scooter in 15 seconds is (ii) Let the car catch up with the scooter in time seconds, then Displacement of scooter in time Displacement of car in time ...(2)
Now, since the scooter has uniform motion, therefore, displacement of scooter We know Therefore, displacement of scooter in time ...(3)
Now, the car has uniform accelerated motion till time and uniform motion beyond that. Therefore, displacement of car in time We know and Therefore, displacement of car in time Therefore, displacement of car in time ...(4) Using relation (2) and equations (3) and (4), we get
02
PYQ 2021
medium
physicsID: jee-main
If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?
1
2
3
4
Official Solution
Correct Option: (2)
To determine the shape of the acceleration-time graph corresponding to the given velocity-time graph with the shape AMB, let's analyze each section of the graph:
The velocity-time graph initially shows a linear increase. This indicates a constant positive acceleration during this interval. Hence, on the acceleration-time graph, this would be represented as a horizontal line above the time-axis (positive acceleration).
At the top of the graph (point M), the velocity reaches a maximum before decreasing. This suggests that the acceleration is zero at this point, as the velocity remains constant momentarily.
Following point M, there is a linear decrease in velocity, indicating a constant negative acceleration. Thus, the acceleration-time graph would represent this as a horizontal line below the time-axis (negative acceleration).
Given these observations, the acceleration-time graph corresponding to the velocity-time graph shape AMB can be visualized as:
The correct option is the second image, where the graph first has a horizontal line in the positive region, then dips to zero, and finally has a horizontal line in the negative region. This accurately reflects the phases of constant positive acceleration, zero acceleration at the peak, and constant negative acceleration as the velocity decreases.
03
PYQ 2022
medium
physicsID: jee-main
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Two identical balls A and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1 and h2 respectively, then
Reason R: Product of said heights.
1
Both A and R are true and R is the correct explanation of A.
2
Both A and R are true but R is NOT the correct explanation of A.
3
A is true but R is false.
4
A is false but R is true.
Official Solution
Correct Option: (1)
The correct Option is(A): Both A and R are true and R is the correct explanation of A.
∴
04
PYQ 2022
medium
physicsID: jee-main
A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will
1
increased by 50%
2
increased by 15%
3
increased by 25%
4
increased by 33%
Official Solution
Correct Option: (1)
The correct option is(A): increased by 50%
⇒ Energy increases by 50%
05
PYQ 2022
easy
physicsID: jee-main
A metal wire of length 0.5 m and cross-sectional area 10–4 m2 has breaking stress 5 × 108 Nm–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms–1
Official Solution
Correct Option: (1)
The problem involves determining the maximum linear velocity of a block tied to a wire before the wire breaks. First, calculate the force that can be sustained by the wire before breaking, using the formula for breaking stress:
Given breaking stress, , and cross-sectional area, , calculate the breaking force:
This force is the maximum tension the wire can withstand. In the case of circular motion, centripetal force is provided by this tension:
where m is the mass (10 kg) and r is the radius (length of the wire = 0.5 m). Set the maximum tension equal to the centripetal force to find the maximum velocity v:
Simplify the equation to solve for v:
Thus, v is calculated as follows:
The computed maximum linear velocity of the block is 50 m/s, which fits within the range [50, 50].
06
PYQ 2022
medium
physicsID: jee-main
From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____ s.
Official Solution
Correct Option: (1)
For case-I : 2nd equations=ut+ H=−u(6)+ g(6)2 H=−6u+18g…(i) For case-II : h=u(1.5)+ g(1.5)2h=1.5u+ …(ii)Multiplying equation (ii) by 4 we get 4h=6u+4.5 g…(iii) equation (i) + equation (iii) we get 5h = 22.5gh=4.5 g… (iv) For case-III :h=0+ gt2…(v)Using equation (4) & equation (5) 4.5g= gt2 t2=9⇒t=3s
07
PYQ 2022
medium
physicsID: jee-main
The electromagnetic waves travel in a medium at a speed of 2.0 × 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be
1
2.25
2
4.25
3
6.25
4
8.25
Official Solution
Correct Option: (1)
The correct option is(A): 2.25.
So
08
PYQ 2022
easy
physicsID: jee-main
A solid cylinder and a solid sphere, having the same mass M and radius R, roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be
1
2
3
4
Official Solution
Correct Option: (4)
= = =
09
PYQ 2022
medium
physicsID: jee-main
Choose the correct answer:
1. Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity u at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of u in ms–1 [use g = 10 ms–2]
1
10
2
15
3
20
4
30
Official Solution
Correct Option: (4)
The correct option is(D): 30 m/s.
Let us assume that they meet at t = t0
⇒ 80 = 2u + 5(2)2
⇒ u= 30 m/s
10
PYQ 2022
medium
physicsID: jee-main
A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping They start from rest The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :
1
2
3
4
Official Solution
Correct Option: (4)
In pure rolling, the point of contact stays stationary relative to the surface, meaning friction causes no displacement. This eliminates the work done by friction, making conservation of mechanical energy a valid approach.
=
=
=
Therefore the correct option is
11
PYQ 2022
easy
physicsID: jee-main
Sand is being dropped from a stationary dropper at a rate of 0.5 kgs–1 on a conveyor belt moving with a velocity of 5 ms–l. The power needed to keep the belt moving with the same velocity will be
1
1.25 W
2
2.5 W
3
6.25 W
4
12.5 W
Official Solution
Correct Option: (4)
The correct option is(D): 12.5 W.
F=2.5
=(2.5)(5)W=12.5 W
12
PYQ 2022
easy
physicsID: jee-main
A longitudinal wave is represented by . The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to
1
2π
2
5π
3
π
4
Official Solution
Correct Option: (2)
The correct option is(B): 5π
Particle velocity
⇒ Maximum particle velocity = (2πn) (10)
⇒ (2πn) (10) = (nλ) (4)
⇒ λ = 5π
13
PYQ 2022
medium
physicsID: jee-main
A particle is moving in a straight line such that its velocity is increasing at 5 ms–1 per meter. The acceleration of the particle is _______ms–2 at a point where its velocity is 20 ms–1.
Official Solution
Correct Option: (1)
a=v =20×5=100 m/sec2
14
PYQ 2022
medium
physicsID: jee-main
Identify the pair of physical quantities that have same dimensions :
1
velocity gradient and decay constant
2
wien’s constant and Stefan constant
3
angular frequency and angular momentum
4
wave number and Avogadro number
Official Solution
Correct Option: (1)
Velocity gradient
=
⇒ Dimensions are
Decay constant has dimensions of because of the relation
⇒ Velocity gradient and decay constant have same dimensions.
15
PYQ 2022
medium
physicsID: jee-main
A stone of mass m tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
1
the same throughout the motion.
2
minimum at the highest position of the circular path.
3
minimum at the lowest position of the circular path.
4
minimum when the rope is in the horizontal position.
Official Solution
Correct Option: (2)
At any :
⇒
Since is constant,
⇒ will be minimum when is minimum.
⇒ corresponds to .
16
PYQ 2022
hard
physicsID: jee-main
A projectile is launched at an angle ‘α’ with the horizontal with a velocity . After , its inclination with horizontal is ‘β’. The value of tanβ will be ( = ).
1
tanα + 5secα
2
tanα– 5secα
3
2tanα– 5secα
4
2tanα + 5secα
Official Solution
Correct Option: (2)
∴
=
Therefore, the correct option is (B):
17
PYQ 2022
hard
physicsID: jee-main
A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of , the rain drops hit herhead vertically. The speed of rain drops with respect to the moving girl is
1
2
3
4
Official Solution
Correct Option: (3)
From graph,
=
=
Therefore, the correct option is (C):
18
PYQ 2022
easy
physicsID: jee-main
A body is projected from the ground at an angle of 45° with the horizontal. Its velocity after is . The maximum height reached by the body during its motion is ________ m. (use = )
Official Solution
Correct Option: (1)
The maximum height reached by the body :
…(i)
…(ii)
19
PYQ 2022
medium
physicsID: jee-main
A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is
1
g/2n
2
g/n
3
2gn
4
g/2n2
Official Solution
Correct Option: (4)
To solve this problem, we will analyze the motion of the balls thrown by the juggler.
Let's denote:
Initial velocity with which each ball is thrown as .
Acceleration due to gravity as (acting downwards).
Time taken for the ball to reach the maximum height as .
According to the problem, the juggler throws the next ball when the first ball reaches its highest position, which implies that balls are thrown per second.
For a ball thrown upwards, at the highest point, the velocity becomes zero. The time to reach this point is given by the first equation of motion:
At the highest point, , so:
The ball should reach the maximum height by the time another ball is thrown, so:
, as balls are thrown per second.
Substitute into :
Now calculate the maximum height using the formula:
Substitute into the equation:
Simplify:
Therefore, the maximum height the balls can reach is .
Hence, the correct option is .
20
PYQ 2022
hard
physicsID: jee-main
A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms–1 and 40 ms–1 respectively. The velocity of the third piece will be
1
15 ms–1
2
25 ms–1
3
35 ms–1
4
50 ms–1
Official Solution
Correct Option: (2)
The correct option is(B): 25 m/s.
Conserving momentum:
21
PYQ 2022
easy
physicsID: jee-main
When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :
1
19.6 m
2
29.4 m
3
39.2 m
4
73.5 m
Official Solution
Correct Option: (2)
The approximate depth of the lake is :
22
PYQ 2022
easy
physicsID: jee-main
A stone tied to a string of length is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed . The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is . The value of is
1
3
2
2
3
1
4
5
Official Solution
Correct Option: (2)
=
23
PYQ 2022
medium
physicsID: jee-main
The root mean square speed of smoke particles of mass 5 \times 10-17 in their Brownian motion in air at NTP is approximately. [Given k = 1.38 \times 10-23 JK-1]
1
60 mm s-1
2
12 mm s-1
3
15 mm s-1
4
36 mm s-1
Official Solution
Correct Option: (3)
To determine the root mean square (RMS) speed of smoke particles in Brownian motion at normal temperature and pressure (NTP), we utilize the formula for the RMS speed of particles in a gas:
where:
is the root mean square speed,
is the Boltzmann constant,
is the temperature in Kelvin, specifically 273 K for NTP,
is the mass of the smoke particle.
Let's calculate step-by-step:
Substitute the values into the formula:
Calculate the numerator:
Calculate the entire expression under the square root:
Now, find the square root of the result:
Convert the answer to mm/s:
Thus, the correct answer is 15 mm s-1.
24
PYQ 2022
easy
physicsID: jee-main
The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x \times 10–4 N. The value of x is _______. [use g = 10 m/s2]
Official Solution
Correct Option: (1)
25
PYQ 2022
medium
physicsID: jee-main
A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____cm. (Velocity of sound in air is 340 ms–1)
Official Solution
Correct Option: (1)
Given
So λ = 100 cm So minimum height is
26
PYQ 2022
medium
physicsID: jee-main
A car covers AB distance with first one-third at velocity v1 ms–1, second one-third at v2 ms–1 and last one-third at v3 ms–1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms–1 ,then the average velocity of the car is ____ ms–1.
Official Solution
Correct Option: (1)
m/sec
27
PYQ 2023
medium
physicsID: jee-main
A car travels a distance of ' ' with speed and then same distance ' ' with speed in the same direction The average speed of the car is:
1
2
3
4
Official Solution
Correct Option: (3)
1. Total distance traveled: 2. Total time taken: 3. Average speed: 4. Simplifying:
Thus, the average speed is . The average speed for equal distances depends on the harmonic mean of the two speeds. This is because the time taken varies inversely with speed.
28
PYQ 2023
easy
physicsID: jee-main
A particle is moving with constant speed in a circular path. When the particle turns by an angle , the ratio of instantaneous velocity to its average velocity is . The value of x will be -
1
7
2
2
3
1
4
5
Official Solution
Correct Option: (2)
Velocity Analysis in Circular Motion
Given:
Time to reach from A to B =
Displacement from A to B =
Now, Average velocity from A to B =
Instantaneous velocity at B is
According to the question,
Conclusion:
The value of is 2.
29
PYQ 2023
hard
physicsID: jee-main
A vehicle travels with speed of and another with speed of , then it's average speed is
1
2
3
4
Official Solution
Correct Option: (1)
The correct answer is (A) : Vav2=31+51=158 ⇒Vav=415=3.75km/h
30
PYQ 2023
easy
physicsID: jee-main
The velocity-time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is:
1
2
3
4
Official Solution
Correct Option: (3)
From the velocity-time graph, we calculate the displacement and total distance traveled:
Displacement: The net displacement is the area under the graph considering direction:
Distance: The total distance is the sum of the absolute areas under the graph:
The ratio of displacement to distance is:
31
PYQ 2023
easy
physicsID: jee-main
The drift velocity of electrons for a conductor connected in an electrical circuit is The conductor in now replaced by another conductor with same material and same length but double the area of cross section The applied voltage remains same The new drift velocity of electrons will be
1
2
3
4
Official Solution
Correct Option: (4)
The drift velocity is given by the formula:
where is the charge of the electron, is the electric field, is the relaxation time, and is the mass of the electron. The drift velocity is independent of the area of cross-section of the conductor. Therefore, the new drift velocity will remain the same as .
32
PYQ 2023
hard
physicsID: jee-main
A body is moving with constant speed, in a circle of radius .The body completes one revolution in 4 s .At the end of 3 rd second, the displacement of body (in mi) from its starting point is :
1
2
3
30
4
Official Solution
Correct Option: (2)
From the given figure above , we get Speed, v = constant Radius, R = 10 m T = Time period = 4s At the end of 3rd second, particle will be at D (Starts from A) displacement S =
So, the correect answer is (B) :
33
PYQ 2023
medium
physicsID: jee-main
The distance travelled by a particle is related to time as The velocity of the particle at is:-
1
2
3
4
Official Solution
Correct Option: (4)
The correct answer is (D) : x=4t2 v=dtdx=8t
At t=5sec v=8×5=40m/s
34
PYQ 2023
medium
physicsID: jee-main
An object moves with speed and along a line segment and respectively as shown in figure Where and , then average speed of the object will be:
1
2
3
4
Official Solution
Correct Option: (2)
35
PYQ 2023
hard
physicsID: jee-main
A horse rider covers half the distance with speed The remaining part of the distance was travelled with speed for half the time and with speed for other half of the time The mean speed of the rider averaged over the whole time of motion is The value of is _____
Official Solution
Correct Option: (1)
The correct answer is 50. tAB= In motion BC x=d1+d2 where d1&d2 we the distance travelled with 10 m/s and 15m/s respectively in equal time intervals 2t′ each d1= ,d2= d1+d2=x= (10+15)= v= =750m/s
36
PYQ 2023
hard
physicsID: jee-main
An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force In the process of its linear motion, the angle (as shown in figure) between the direction of force and horizontal varies as , where is a constant and is the distance covered by the object from its initial position The expression of kinetic energy of the object will be The valte of is
Official Solution
Correct Option: (1)
37
PYQ 2023
medium
physicsID: jee-main
A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of train B is 54 km/h, then the length of train B is:
1
100 m
2
320 m
3
200 m
4
400 m
Official Solution
Correct Option: (2)
The velocity of train A ( ) is given as , which can be converted to SI units: The velocity of train B ( ) is given as : Since the trains are moving in opposite directions, the relative velocity ( ) is the sum of their velocities: The time of crossing ( ) is given as . The length of train B ( ) is related to the time of crossing and relative velocity as: Substituting the values: Solving for : Thus, the length of train B is .
38
PYQ 2023
hard
physicsID: jee-main
For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown in below figure, the projection of OP on the x-axis at time t is
1
x(t) = rcos (\omega t )
2
x(t) = rcos (\omega t - \omega )
3
x(t) = rcos (\omega t + )
4
x(t) = rsin (\omega t + )
Official Solution
Correct Option: (3)
Let the particle revolve around the center with a uniform angular velocity . The angular displacement of the particle at time is:
From the figure, the angle of the particle from the -axis at is . Hence, at time , the total angle with respect to the -axis is:
The projection of on the -axis is given by:
Substitute :
Final Answer: The projection of on the -axis is:
39
PYQ 2023
medium
physicsID: jee-main
Given below are two statements: Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II: Area under acceleration-time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.
1
Statement I is incorrect but Statement II is True.
2
Both Statement I and Statement II are False.
3
Statement I is correct but Statement II is false.
4
Both Statement I and Statement II are true.
Official Solution
Correct Option: (4)
Step 1: Analyze Statement I. The velocity is given by: Integrating both sides with respect to time: The area under the velocity-time ( - ) graph gives displacement. Hence, Statement I is true. Step 2: Analyze Statement II. The acceleration is given by: Integrating both sides with respect to time: The area under the acceleration-time ( - ) graph gives the change in velocity. Hence, Statement II is also true. Final Answer: Both statements are:
40
PYQ 2023
medium
physicsID: jee-main
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm2. The area of cross section at the oulet is 10 mm2. If the piston is pushed at a speed of 4 cm s-1, the speed of outgoing fluid is ______ cm s-1.
Official Solution
Correct Option: (1)
By the equation of continuity:
Where and are the areas of cross-section at the piston and the outlet, and and are the velocities at the piston and the outlet respectively. Given:
Substituting in the continuity equation:
Solving for :
Thus, the speed of the outgoing fluid is 80 cm/s .
41
PYQ 2023
medium
physicsID: jee-main
A person travels x distance with velocity v1 and then x distance with velocity v2 in the same direction. The average velocity of the person is v, then the relation between v, v1 and v2 will be
1
2
V=V1+V2
3
<
4
Official Solution
Correct Option: (4)
Let the person travels the first distance with velocity , and the next distance with velocity . The time taken for the first part of the journey is:
The time taken for the second part of the journey is:
The total displacement is and the total time is:
The average velocity is given by:
Thus, the relation is:
42
PYQ 2023
medium
physicsID: jee-main
A current of 2 A flows through a wire of crosssectional area 25.0 mm2 . The number of free electrons in a cubic meter are 2.0 x 1028 . The drift velocity of the electrons is _____ x 10-6 ms-1 (Given, charge on electron = 1.6 x 10-19C)
Official Solution
Correct Option: (1)
Step 1: Use the formula for drift velocity - Drift velocity is given by: where is the current, is the number of free electrons per unit volume, is the electron charge, and is the cross-sectional area.
Step 2: Substitute the values - Simplifying:
Final Answer: The drift velocity of the electrons is 25 × 10⁻⁶ m/s.
43
PYQ 2023
medium
physicsID: jee-main
A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound: 330 m/s) approximate difference of frequencies heard by the person will be:
1
33 Hz
2
10 Hz
3
55 Hz
4
80 Hz
Official Solution
Correct Option: (3)
Frequency Observed (Doppler Effect):
The observed frequency for train A (approaching):
The observed frequency for train B (receding):
Difference in Frequencies:
Final Answer:
44
PYQ 2023
easy
physicsID: jee-main
Match List I with List II List I List II A. Spring constant I. (T-1) B. Angular speed II. (MT-2) C. Angular momentum III. (ML2) D. Moment of Inertia IV. (ML2T-1)
List I
List II
A
Spring constant
I
(T-1)
B
Angular speed
II
(MT-2)
C
Angular momentum
III
(ML2)
D
Moment of Inertia
IV
(ML2T-1)
Choose the correct answer from the options given below:
1
A-I, B-III, C-II, D-IV
2
A-II, B-I, C-IV, D-III
3
A-IV, B-I, C-III, D-II
4
A-II, B-III, C-I, D-IV
Official Solution
Correct Option: (2)
Solution: Spring constant:
The spring constant is given by: Thus, spring constant has units of , which corresponds to List II.
Angular speed:
The angular speed has dimensions: Thus, angular speed has dimensions , corresponding to List I.
Angular momentum:
Angular momentum is given by:
Thus, Angular momentum has dimensions , corresponding to List III.
Moment of inertia:
The moment of inertia is: Thus, moment of inertia has dimensions , corresponding to List IV.
Thus, the correct match is .
45
PYQ 2023
medium
physicsID: jee-main
A particle is thrown vertically upward with initial velocity of 150 m/s. Find the ratio of its speed at t = 3 seconds and t = 5 seconds. is the value of x is___. (take g = 10 m/s2)
1
5
2
6
3
10
4
-5
Official Solution
Correct Option: (1)
The correct option is(A): 5
46
PYQ 2023
medium
physicsID: jee-main
An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is
1
2
3
4
Official Solution
Correct Option: (4)
The correct option is(D):
47
PYQ 2023
medium
physicsID: jee-main
Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of the motion of the source. D. The speed of light in a medium is independent of intensity. Choose the correct answer from the options given below:
1
C and D only
2
B and D only
3
B and C only
4
A and C only
Official Solution
Correct Option: (1)
Analysis of Statements:
A: Incorrect. The speed of light in vacuum does not depend on the direction of propagation.
B: Incorrect. Speed of light in a medium depends on the wavelength (dispersion).
C: Correct. The speed of light is constant in vacuum, independent of the source’s motion.
D: Correct. The speed of light in a medium is not affected by light intensity.
Final Answer:
48
PYQ 2023
medium
physicsID: jee-main
The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
1
2:1
2
1:√2
3
4:1
4
1:4
Official Solution
Correct Option: (1)
The correct option is(A): 2:1
49
PYQ 2023
medium
physicsID: jee-main
The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at A is 1.5 cm², and B is is 25 mm², if the speed of liquid at B is 60 cm/s then is: (Given and are liquid pressures at A and B points. density A and B are on the axis of tube)
1
27 Pa
2
175 Pa
3
135 Pa
4
36 Pa
Official Solution
Correct Option: (2)
To determine the pressure difference between points A and B in the horizontal tube, we can apply the Bernoulli's Equation for incompressible and steady flow:
Rearranging the equation to find :
Step 1: Convert Units
First, convert all measurements to SI units.
- Cross-sectional areas:
- Speed at B:
Step 2: Apply Continuity Equation
For steady, incompressible flow, the continuity equation states:
Solving for :
Step 3: Calculate Pressure Difference
Given the density of the liquid , substitute the known values into the Bernoulli's equation:
Therefore, the pressure difference is 175 Pa.
50
PYQ 2023
medium
physicsID: jee-main
The rms speed of oxygen molecule in a vessel at particular temperature is , where is the average speed of the molecule. The value of x will be : (Take )
1
4
2
8
3
27
4
28
Official Solution
Correct Option: (4)
The relationship between rms speed , average speed , and is given as:
From the kinetic theory of gases, the rms speed and average speed are related as:
Taking the ratio:
Substitute :
Equating this to the given relation:
Square both sides:
Simplify:
Solve for :
51
PYQ 2023
hard
physicsID: jee-main
To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____KJ. [The coefficient of friction between tyre of bus and road is 0.04].
Official Solution
Correct Option: (1)
For constant speed, work done by the engine + work done by friction (by Work-Energy Theorem). Thus, we can write:
where , , , and . So,
Thus, the work done by the engine is 784 KJ.
52
PYQ 2023
medium
physicsID: jee-main
The speed of a wave produced in water is given by v= . Where λ,g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are:
1
1,1,0
2
3
4
1,-1,0
Official Solution
Correct Option: (3)
Understanding the Problem
We are given that the speed of a wave ( ) depends on wavelength ( ), acceleration due to gravity ( ), and density ( ). We need to find the exponents , , and in the equation:
Dimensional Analysis
1. Dimensional Formulas:
(velocity)
(wavelength)
(acceleration)
(density)
2. Substitute into the Equation:
3. Simplify:
4. Equate Powers:
(from )
(from )
(from )
Solving the Equations
1. From the equation:
2. From the equation:
3. Substitute and into the equation:
Final Answer
The values of , , and are:
53
PYQ 2024
medium
physicsID: jee-main
For a motion, relation between position x and time is Find the relation between velocity and acceleration .
1
2
3
4
Official Solution
Correct Option: (3)
The Correct Option is (C):
54
PYQ 2024
hard
physicsID: jee-main
A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:
1
5 m/s
2
4 m/s
3
2 m/s
4
6 m/s
Official Solution
Correct Option: (1)
To solve the problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces are acting on it.
Step-by-step Solution:
Calculate the initial momentum of the body:
The initial mass of the body is and its initial velocity is . Thus, the initial momentum ( ) is given by:
Calculate the final momentum of the system:
After adding 200 kg, the total mass becomes . Let the final velocity be . The final momentum ( ) is expressed as:
Apply the conservation of momentum:
According to the conservation of momentum:
Solve for :
Rearrange the equation for :
Thus, the final velocity of the body after adding 200 kg extra mass is 5 m/s.
Conclusion: The correct answer is , which matches option
5 m/s
. This result confirms that option
5 m/s
is the correct choice.
55
PYQ 2024
medium
physicsID: jee-main
A ball is released from a height of on a fixed smooth hemispherical surface as shown. Find its velocity when it is at a height of from ground. (take = )
1
2
3
4
Official Solution
Correct Option: (3)
The Correct Option is (C):
56
PYQ 2024
medium
physicsID: jee-main
A uniform disk of mass is rolling without slipping with a speed of . Find minimum energy required to bring the disk to rest (in ).
Official Solution
Correct Option: (1)
The Correct Answer is :
57
PYQ 2024
medium
physicsID: jee-main
A ball of mass moving with initial velocity is stopped by an external force in . Find value of in newton :
Official Solution
Correct Option: (1)
The correct answer is :
58
PYQ 2024
medium
physicsID: jee-main
Two trains run on North-South parallel tracks. Train A moves with velocity 20 m/s towards North and train B moves with velocity 30 m/s towards South. Then find the velocity of train B with respect to train A
Official Solution
Correct Option: (1)
The correct answer is : 50 m/s
59
PYQ 2024
hard
physicsID: jee-main
Consider a series of steps as shown. A ball is thrown from 0. Find the minimum speed to directly jump to 5th step
1
2
3
4
Official Solution
Correct Option: (3)
The Correct option is (C):
(2.5,2.5) must lie on this
[ Happens when ]
60
PYQ 2025
medium
physicsID: jee-main
Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:
1
5.6
2
2.8
3
11.2
4
8.4
Official Solution
Correct Option: (1)
Step 1: Given Escape Velocity Formula
The escape velocity is given by the formula:
Step 2: Given Mass and Radius Relationships
We are given the following mass and radius relationships:
Step 3: Calculate the Ratio of Escape Velocities
The ratio of the escape velocities is:
Step 4: Calculate the Escape Velocity from the Planet
Therefore, the escape velocity from the planet is:
