Question

A block of mass $m$ is moving with a constant acceleration $a$ on a rough horizontal plane. If the coefficient of friction between the block and ground is $\mu$, the power delivered by the external agent after a time $t$ from the beginning of motion is

• A. $m{a}^{2}t$
• B. $\mu mgat$
• C. $\mu m(a+\mu g)gt$
• D. $m(a+\mu g)at$

Answer 1

The correct option is D $m(a+\mu g)at$

Let $F$ be the force applied by the external agent.

Let $v$ be the speed of the block at the time $t$

Instantaneous power delivered, $P=\overrightarrow{F}.\overrightarrow{V}$

Applying Newton's second law,

$F-f=ma$

$\Rightarrow F=f+ma$

$\Rightarrow$ $P=(f+ma)v$

$f=\mu mg$

Also, $v=at(\because u=0)$

$\therefore P=(\mu mg+ma)v=m(a+\mu g).at$

Hence, option $\left(d\right)$ is the correct answer.