A smooth block is released at rest on a `45^(@)` incline and then slides a distance 'd'. The time taken to slide is 'n' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

Options

A. `mu_(k)=1-(1)/(n^(2))`
B. `mu_(k)=sqrt(1-(1)/(n^(2)))`
C. `mu_(s)=1-(1)/(n^(2))`
D. `mu_(s)=sqrt(1-(1)/(n^(2)))`

Answer

a

Explanation

On smooth incline plane
`d=(1)/(2)g sinn theta xxt^(2)`
On rough incline plane
`d=(1)/(2)g(sin theta-mu_(k) cos theta) (nt)^(2)...(b)`
Solving equations (a)and(b)
`sin theta=n^(2)(sintheta-mu_(k) cos theta)`and Putting `theta=45^(@)`
we get `mu_(k)=1-(1)/(n^(2))`