A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is
1
20J
2
30J
3
-30J
4
-60J
Official Solution
Correct Option: (2)
as process is isochoric.
For CA process,
The graph given is inconsistent with the statement BC may be adiabatic and CA cannot be like isobaric as shown, as increasing volume while rejecting heat at same time.
02
PYQ 2022
medium
physicsID: jee-main
A proton, a neutron, an electron and an α-particle have same energy. If λp, λn, λe and λα are the de Broglie’s wavelengths of proton, neutron, electron and α particle respectively, then choose the correct relation from the following:
1
λp = λn > λe > λα
2
λα < λn < λp < λe
3
λe < λp = λn > λα
4
λe = λp = λn = λα
Official Solution
Correct Option: (1)
The correct option is(B): λα < λn < λp < λe.
de Broglie wavelength
Where K: kinetic energy
⇒ For some K,
Since mα > mn > mp > me
⇒ λα < λn < λp < λe
03
PYQ 2023
medium
physicsID: jee-main
A ball of mass rests on a vertical post of height A bullet of mass , travelling in horizontal direction, hits the centre of the ball After collision both travels independently The ball hits the ground at a distance and the bullet at a distance of from the foot of the postThe value of initial velocity of the bullet will be (if ) :
Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is m. The value of the x is _____. (1eV = 1.6 x 10-19J, = 9 x 109 NM2 / C2 and electronic charge = 1.6 x 10-19JC)
Official Solution
Correct Option: (1)
05
PYQ 2023
hard
physicsID: jee-main
The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is______ mm2 . (Given, y = 2.0 x 1011 Nm-2)
Official Solution
Correct Option: (1)
The elastic potential energy stored in a stretched wire is given by: where:
(elastic potential energy)
(length of the wire)
(extension in the wire)
(Young's modulus of steel)
is the cross-sectional area of the wire (to be calculated)
Rearranging the formula for : The force is given by: Substitute back into the equation for : Substitute the given values: Simplify: Convert to :
06
PYQ 2023
medium
physicsID: jee-main
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be
1
1
2
2
3
3
4
4
Official Solution
Correct Option: (3)
The correct option is(C): 3
07
PYQ 2024
medium
physicsID: jee-main
Determine Min. Energy released when an electron jumps to ground state in Balmer series from infinity.
Official Solution
Correct Option: (1)
The Correct Answer is :
08
PYQ 2026
medium
physicsID: jee-main
A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height . The value of is _________.
1
2
2
4
3
3
4
6
Official Solution
Correct Option: (2)
To find the value of , we utilize the principles of conservation of mechanical energy and circular motion dynamics.
First, let's consider the energy of the body. Since the plane and the loop are smooth, there is no work done by friction. The total mechanical energy is conserved throughout the motion. Let the reference level for potential energy ( ) be the lowest point of the loop. At the initial point on the inclined plane, the body is released from height at rest ( ). Initial Mechanical Energy,
At the highest point of the vertical circle, the height is (the diameter of the circle). Let the velocity of the body at this point be . Final Mechanical Energy, By the Law of Conservation of Energy, :
$ mg N 3mg N = 3mg N = 3mg v^2 g h = \alpha R \alpha = 4$. This corresponds to option 2.
