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 measurement of work done by the force $F_0$

Answer 1

Answer: (A), (C)

The correct options are
A Both will measure the same work
C Girl will measure higher value than the boy

Work done $=\int \overrightarrow{F}.\overrightarrow{\delta }s$.

Lets assume particle moved $x$ (in $m$) during time, $t_o$ in frame of train.

Then work done in train frame, $W_{train}=Fx$

Work done measured by girl , $W_g=F_{0}x$

lets assume distance travelled by particle in ground frame $x+C$ where $C=t_o\times trainspeed$

Work done measured by $W_b=F_0(x+C)$ where $C$ come due to the train motion.

thus, $W_b>W_g$ and as the data insufficient so we can't measure work done by $F_0$.

so incorrect option (A), (C).