A given object takes n times as much time to slide down a `45^(@)` rough incline as it takes to slide down a perfectly smooth `45^(@)` incline. The coefficeint of kinetic friction between the object and the incline is given by:

Options

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

Answer

A

Explanation

`l=(1)/(2)( g sin theta)_(1)^(2) l=(1)/(2)(g sin theta- mug cos theta)t_(2)^(2)`
`t_(2)=nt_(1)`
`sin theta=(sin theta- mu cos theta)n^(2)`
`(2)/sqrt(2)=((1)/sqrt(2)-muxx(1)/sqrt(2))n^(2) therefore mu=1-(1)/n^(2))`