WBJEE 2023 Physics & Chemistry Solved Paper

1. Train Frame (the frame of reference of the girl on the train):
- The initial velocity of the ball is 0 (it's at rest before she throws it).
- The final velocity of the ball is v (after she throws it).
- So the kinetic energy (K.E.) of the ball in the train frame, after she throws it, is ‌

1

2

mv2.
- The work done by the girl is equal to the change in kinetic energy, so it's also ‌

1

2

mv2.
2. Ground Frame (the frame of reference of a person standing by the track) :
- The initial velocity of the ball is u (equal to the speed of the train, as the ball is at rest relative to the train before she throws it).
- The final velocity of the ball is u+v (the speed of the train plus the speed of the ball relative to the train).
- So, the kinetic energy (K.E.) of the ball in the ground frame, after she throws it, is ‌

1

2

m(u+v)2=‌

1

2

mu2+‌

1

2

mv2+muv.
- The gain in K.E. of the ball as measured by a person standing on the ground is the final K.E. minus the initial K.E., which is ‌

1

2

mu2+‌

1

2

mv2+muv−‌

1

2

mu2=‌

1

2

mv2+muv. This corresponds to the work done by the girl plus the work done by the train.
So, in conclusion:
- Option A is correct.
- Option B is correct.
- Option C is correct.
- Option D is incorrect because it's missing the term for the work done by the train (muv).