A given object taken double time to slide down a `45^(@)` rough incline as it takes to slide down a perfectly smooth `45^(@)` incline. The coefficient of kinetic friction between the object and the incline is given by

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `(3)/(4)`
D. `(1)/(sqrt2)`

Answer

C

Explanation

`sqrt((2s)/(g sin 45^(@) - mu g cos 45^(@))) = 2 xx sqrt((2s)/(g sin 45^(@)))`
`(1)/(((1)/(sqrt2) - (mu)/(sqrt2))) = (4)/(((1)/(sqrt2)))`
`1 = 4 (1 - mu)`
`mu = (3)/(4)`