question_answer

To determine the coefficient of friction  between a rough surface and a block, the surface is kept inclined at \[{{45}^{o}}\] 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 112 in moving down the same distance d. The coefficient of friction is

A)  3/4    

B)  5/4    

C)  1/2   

D)  \[1/\sqrt{2}\]

Correct Answer: A

Solution :

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