Question

A block of mass $m$ is pulled by a constant power $P$ placed on a rough horizontal plane. The friction coefficient between the block and surface is $\mu .$ Find the maximum velocity of the block.

• A. $\frac{P}{\mu mg}$
• B. $\frac{P}{2\mu mg}$
• C. $\frac{P}{4\mu mg}$
• D. $\frac{2P}{\mu mg}$

Answer 1

Answer: (A)

$\frac{P}{\mu mg}$

Power P=F.v=constant $\Rightarrow F=\frac{P}{v}orF\propto \frac{1}{v}$
as $v$ increases, $F$ decreases.
when $F=\mu mg,$ net force on block becomes zero, i.e., it has maximum or terminal velocity
$\therefore P=\left(\mu mg\right)v_{max}or{v}_{max}=\frac{P}{\mu mg}$