Question

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at ${45}^0$ 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:

• A. $3/4$
• B. $5/4$
• C. $1/2$
• D. $1/\sqrt{2}$

Answer 1

The correct option is A $3/4$

If the same wedge is made rough then time taken by it to come down becomes $n$ times more. The coefficient of friction
$\mu =[1-\frac{1}{n^2}]\tan \theta \Rightarrow \mu =[1-\frac{1}{2^2}]\tan {45}^0$
$\mu =\frac{4-1}{4}\Rightarrow \mu =\frac{3}{4}$