A body is moving is down an inclined plane of slope `37^@` the coefficient of friction between the body and the plane varies as `mu=0.3x`, where x is the distance traveled down the plane by the body. The body will have maximum speed. `(sin 37^@ =(3)/(5))` .

Options

A. at x = 1.16 m
B. at x = 2 m
C. at bottommost point of the plane
D. at x = 2.5 m

Answer

D

Explanation

When block will cross position of equilibrium, then its speed will be maximum.
So, `N= mg cos 37^@ .......(i) `
and, `mg sin 37^@ = muN....... (ii)`
By equation (i) and (ii)
`mg sin 37^@ = 0.3x (mg cos 37^@)`
Which gives x= 2.5 m