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

Options

A. `v = (P)/(mg sin theta+mu mg cos theta)`
B. `v =(P)/(mg sin theta-mumg cos theta)`
C. `v=(2P)/(mg sintheta-mu mg cos theta)`
D. `v = (3P)/(mg sin theta - mu mg cos theta)`

Answer

A

Explanation

Let at any time the speed of the block along the incline upwards be `v`.
`(P)/(v) -mg sin theta - mu mg cos theta = (mdv)/(dt)`
the speed is maximum when `(dv)/(dt) = 0`
`:. v_(max) =(P)/(mg sin theta+mu mg cos theta)`.