Question

A body takes time t to reach the bottom of an inclined plane of angle θ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is

• A. $\frac { 3 } { 4 } \tan \theta$
• B. $\frac { 2 } { 3 } \tan \theta$
• C. $\frac { 1 } { 4 } \tan \theta$
• D. $\frac { 1 } { 2 } \tan \theta$

Answer 1

Answer: (A)

$\frac { 3 } { 4 } \tan \theta$

Answer 2

$\mu = \tan \theta \left( 1 - \frac { 1 } { n ^ { 2 } } \right)$ $= \tan \theta \left( 1 - \frac { 1 } { 2 ^ { 2 } } \right) = \frac { 3 } { 4 } \tan \theta$