Question

The time taken by a body to slide down a rough `45^(@)` inclined plane is twice that required to slide down a smooth `45^(@)` inclined plane. The coefficient of kinetic friction between the object and rough plane is given by
A. `(1)/(3)`
B. `(3)/(4)`
C. `sqrt((3)/(4))`
D. `sqrt((2)/(3))`

Answer 1

Correct Answer - B
`t = sqrt((25)/(a)) prop (1)/sqrt(a)`
`:. (t_(1))/(t_(2)) = sqrt((a_(2))/(a_(1)))`
`(2)/(1) = sqrt((g sin theta )/(g sin theta - mu_(K) g cos theta)) = sqrt((1)/(1 - mu_(K)))`
as `sin theta = cos theta `at `45^(@)`
On solving the above equation, we get
`mu_(K) = (3)/(4)`