A body of mass 'm' slides down a smooth inclined plane having an inclination of `45^(@)` with the horizontal. It takes 2S to reach the bottom. It the body is placed on a similar plane having coefficient friction 0.5 What is the time taken for it to reach the bottom ?

Explanation

Mass = m, `= 45^(@)`
Time taken to reach the bottom `T_(1)=2 sec mu = 0.5`
Time taken by the body to touch the bottom without friction is `T_(1)=sqrt((2l)/(g sin theta))`
Time taken with friction is `T_(2)= sqrt((2l)/(g(sin theta - mu cos theta)))`
`(T_(1))/(T_(2))=sqrt((sin theta - mu cos theta)/(sin theta))`
`T_(2)=T_(1)sqrt((sin theta)/(sin theta - mu cos theta))=2.828 sec`.