Question

Consider two observers moving with respect to each other at a constant speed $v$ along a straight line. They observe a block of mass $m$ moving a distance $l$ on a rough surface. Then which of the following quantities will be same as observed by the two observers:

• A. kinetic energy of the block at time $t$
• B. work done by friction
• C. total work done on the block
• D. acceleration of the block

Answer 1

The correct option is D acceleration of the block

Due to relative motion between observers, they will find the block moving the different speeds.
$\therefore$Kinetic energy observed by each observer will be different at any time $t$.

$\Rightarrow$The direction of motion of block is not given w.r.t to observers, hence they may observe different work done by friction on the block.

$\Rightarrow$Velocity of block as observed by both observers are different. So for them $\Delta K.E$ will be different. Hence, from work-energy theorem the net workdone on block won't be same for both observers.

$\because$ Both observers are moving with constant speed, hence the rate of change of velocity of block with respect to time will be $\text{zero}$, as observed by any of the observer.
$\therefore {\overrightarrow{a}}_{\text{block, observer}}=0=\text{constant}$
$\Rightarrow$Option $\left(d\right)$ is correct.