Question

If a person is pushing a box inside a moving train, the work done in the frame of earth will be:
${\overrightarrow{S}}_0=$ displacement of the train relative to ground.
$\overrightarrow{S}=$ displacement of the box w.r.t. train.

• A. Zero
• B. $\overrightarrow{F}.(\overrightarrow{S}+{\overrightarrow{S}}_0)$
• C. $\overrightarrow{F}.\overrightarrow{S}$
• D. $\overrightarrow{F}.{\overrightarrow{S}}_0$

Answer 1

The correct option is B $\overrightarrow{F}.(\overrightarrow{S}+{\overrightarrow{S}}_0)$

Work done in frame of earth,
$W=\overrightarrow{F}.{\overrightarrow{S}}_g$
where,
${\overrightarrow{S}}_g=$ displacement of the box w.r.t ground.
$\therefore$ According to question,
$\overrightarrow{S}={\overrightarrow{S}}_g-{\overrightarrow{S}}_0$
$\Rightarrow {\overrightarrow{S}}_g=(\overrightarrow{S}+{\overrightarrow{S}}_0)$
$\therefore$ Work Done $=\overrightarrow{F}.(\overrightarrow{S}+{\overrightarrow{S}}_0)$