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

Options

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

Explanation

`t_(1)=sqrt((2d)/(g sin45^(@)))=sqrt((2d)/((g)/sqrt(2)))`
`t_(2)=sqrt((2d)/(((g)/(sqrt(2))-mu(g)/(sqrt(2))))`
`t_(2)=nt_(1)`
`sqrt((2d)/(((g)/(sqrt(2))-mu(g)/(sqrt(2)))))=nsqrt((2d)/((g)/(sqrt(2))))`
`(1)/(sqrt(1-mu))=n`
`(1)/(1-mu)=n^(2)`
`1 = n^(2)-n^(2)mu`
`(1)/(n^(2))=-1-mu`
`mu=(1-(1)/(n^(2)))`