When a body slides down from rest along a smooth inclined plane making an angle of 45^(@) with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the coefficient of friction between the body and the rough plane.

When a body slides down from rest along a smooth inclined plane making

1.	When a body slides down from rest along a smooth inclined plane making an angle of 45^(@) with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the coefficient of friction between the body and the rough plane.
Answer» Solution :When slopeis smoothas shownin figureboydslidesonslope `F = ma` `F= mg SIN theta ` `a= g sin theta ` `theta= 45^(@)` `a= g (1)/(SQRT(2))` Letdistancecovered by bodybe dd =mt + `(1)/(2 ) at^(2)` ` d= (1)/(2) ( g)/(sqrt(2))t^(2)` `d= (gt^(2))/(2sqrt(2))` Heret = pt d= - (p T ) `+(1)/(2) ` a(p T ) COMPARING (1) and (2) `(1-mu ) p^(2) =1` `1-mu = (1)/( p^(2))` `mu= 1= (1)/(p^(2))`