A given object takes m times as much time to slide down a `45^(@)` rough incline as it takes to slide down a perfectly smooth `45^(@)` incline. The coefficient friction between the objected and the incline is given by

Options

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

Explanation

`S=(1)/(2)((g)/sqrt(2))t^(2)` ,
`S=(1)/(2)((g)/sqrt(2)-(mug)/sqrt(2))(tm)^(2)`

`1=(1-mu_(k))m^(2)rArr mu_(k)=1-(1)/(m^(2))`