To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at `45^(@)` and the block is released from rest. The block takes a time t in moving a distance d. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time t/2 in moving down the same distance d. The coefficient of friction is

Options

A. `3//4`
B. `5//4`
C. `1//2`
D. `1//sqrt(2)`

Answer

A

Explanation

( a) If the same wedge is made rough, then time taken by it come down becomse n times more. The coefficient of friction.

For rough surface
`t=sqrt((2s)/(2 sin theta-mu g cos theta))`……(i)
For smooth surface
`(t)/(n)=sqrt((2s)/(g sin theta))`....(ii)
From Eqs. (i) and (ii) we have
`mu =(1-(1)/(n^(2))) tan theta`
`therefore mu =[1-(1)/(n^(2))] tan theta=[1-(1)/(2^(2))] tan 45^(@)`
`implies mu=(4-1)/(4)=(3)/(4)`