A body slides down from rest along a smooth inclined plane making an angle of `45^(@)` with the horizontal and takes time 'Y' to slide down the whole length of the plane. If the plane surface is rough the same body takes n.t time to slide down same length of the plane where n is a number greater than one. What is the value of coefficient of friction between the body and rough plane surface?

Options

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

Answer

a

Explanation

Here applying `S = ut + (1)/(2)at^(2)`
and putting u = 0, we get For smooth inclined plane `theta = 45^(@)`
`|a|= g sin theta= g//sqrt/2`
Now ` t_(1)=sqrt((2s)/(a))=sqrt((2sqrt(2))/(g))`
For rough plane `a = g sin theta-mu g cos theta=g//sqrt2-(mu)/(sqrt2)`
`=(g(1-mu))/(sqrt2)`
and `t_(2)=sqrt((2S.sqrt2)/(g(1-mu)))=sqrt(2sqrtS)/(g(1-mu))`
Dividing `(1)/(1-mu)=n^(2)`
`:.1-mu=(1)/(n^(2))`
or`mu=1-1//m^(2)`
Hence (a) is the corect choice