Question

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at $45^{\circ}$ 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. 44624
• B. 44685
• C. 44563
• D. $1/\sqrt{2}$

Answer 1

The Correct Option is A

If the same wedge is made rough then time taken by it to come down becomes $n$ times more. The coefficient of friction

$\mu=\left[1-\frac{1}{n^{2}}\right] \tan \theta$ $ \Rightarrow \mu=\left[1-\frac{1}{2^{2}}\right] \tan 45^{\circ}$ $\mu=\frac{4-1}{4}$ $ \Rightarrow \mu=\frac{3}{4}$