Question

A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is given by

• A. $\left( 1 - \frac { 1 } { n ^ { 2 } } \right)$
• B. $\frac { 1 } { 1 - n ^ { 2 } }$
• C. $\sqrt { \left( 1 - \frac { 1 } { n ^ { 2 } } \right) }$
• D. $\sqrt { \frac { 1 } { 1 - n ^ { 2 } } }$

Answer 1

Answer: (A)

$\left( 1 - \frac { 1 } { n ^ { 2 } } \right)$

Answer 2

$\mu = \tan \theta \left( 1 - \frac { 1 } { n ^ { 2 } } \right)$ $= 1 - \frac { 1 } { n ^ { 2 } }$ [As $\theta = 45 ^ { \circ }$ ]