Question

Two frames, one stationary and the other moving, are initially coincident. Two observers in the two frames observe a body initially at rest in the coincident frame. A constant force $F$ starts acting on the body along horizontal axis, when moving frame starts to separate from the fixed frame. Work done $W$ as observed by the stationary frame and $W^{\prime }$ as observed from the moving frame are compared to the each other as:

• A. $W=W^{\prime }$
• B. $W\ne W^{\prime }$
• C. $W=\frac{1}{2}{W}^{\prime }$
• D. $W=2W^{\prime }$

Answer 1

Answer: (B)

$W\ne W^{\prime }$

Let $u$ be the speed of moving frame.
If the horizontal distance covered by the body at any instant w.r.t. moving frame is $x$, then distance covered by the body w.r.t stationary frame is $(x+ut)$.
Force '$F$' remains the same w.r.t both the frames.
Work done w.r.t. stationary frame W
$=F(x+ut)=Fx+Fut$
But $Fx$ is the work done w.r.t. moving frame
$\therefore W=W^{\prime }+Fut$
i.e. $W\ne W^{\prime }$