Q157 / 200 · WBJEE 2014 · Physics
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
- Correct answerA$3 / 4$
- B$5 / 4$
- C$1 / 2$
- D$1 / \sqrt{2}$
Solution
If the same wedge is made rough then time taken by it to come down becomes $n$ times more. The coefficient of friction 
$$
\begin{array}{l}
\mu=\left[1-\frac{1}{n^{2}}\right] \tan \theta \Rightarrow \mu=\left[1-\frac{1}{2^{2}}\right] \tan 45^{\circ} \\
\mu=\frac{4-1}{4} \Rightarrow \mu=\frac{3}{4}
\end{array}
$$
$$
\begin{array}{l}
\mu=\left[1-\frac{1}{n^{2}}\right] \tan \theta \Rightarrow \mu=\left[1-\frac{1}{2^{2}}\right] \tan 45^{\circ} \\
\mu=\frac{4-1}{4} \Rightarrow \mu=\frac{3}{4}
\end{array}
$$Hence, the correct answer is option: 'A'.