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. (a) `(P)/(mg sin theta+mu mg cos theta)`
B. (b) `(P)/(mg sin theta-mu mg cos theta)`
C. (c) `(2P)/(mg sin theta-mumgcostheta)`
D. (d) `(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.
Then from Newton's second law,
`P/v-mg sin theta-mu mg cos theta=(mvdv)/(dt)`
The speed is maximum when `(dv)/(dt)=0`
`v_(max)=(P)/(mg sin theta+mu mg cos theta)`