Question

A particle of mass $m$ is at rest in a train moving with constant velocity with respect to ground. Now the particle is accelerated by a constant force $F_0$ acting along the direction of motion of train for time $t_0$. A girl in the train and a boy on the ground measure the work done by this force. Which of the following are INCORRECT?

• A. Both will measure the same work
• B. Boy will measure higher value than the girl
• C. Girl will measure higher value than the boy
• D. Data is insufficient for the comparison of work done by the force $F_0$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Both will measure the same work
C Girl will measure higher value than the boy
D Data is insufficient for the comparison of work done by the force $F_0$

Using the formula $W=\overrightarrow{F}.\overrightarrow{s}$
$W=Fs\cos 0$
$W=Fs$
Let $v_0$ be the velocity of train
$W_F$ w.r.t. girl $=F_0.\frac{1}{2}\left(\frac{F_0}{m}\right)t_0^2$
$W_F$ w.r.t. boy $=F_0[\frac{1}{2}\left(\frac{F_0}{m}\right)t_0^2+v_0{t}_0]$
$(W_{\text{boy}}>W_{\text{girl}})$