Question

A block of mass $m$ is being pulled up a rough incline by an agent delivering constant power $P$. The coefficient of friction between the block and the incline is $\mu$. The maximum speed of the block during the course of ascent is

• A. $v=\frac{P}{mg\sin \theta +\mu mg\cos \theta }$
• B. $v=\frac{P}{mg\sin \theta -\mu mg\cos \theta }$
• C. $v=\frac{2P}{mg\sin \theta -\mu mg\cos \theta }$
• D. $v=\frac{3P}{mg\sin \theta -\mu mg\cos \theta }$

Answer 1

Answer: (A)

$v=\frac{P}{mg\sin \theta +\mu mg\cos \theta }$

Since power applied is constant

$=P=F\times v$.

Maximum velocity will be when net force applied is equal and opposite to the force on body along the inclined surface.

Net force

$F=F_g+F_f=mgsin\theta +\mu \times [N=mgcos\theta ]$.

Hence $v=\frac{P}{F}=\frac{P}{mgsin\theta +\mu mgcos\theta }$ is the maximum attainable velocity.