Q. A given object taken $n$ times as much time to slide down a $45{^\circ}$ rough incline as it takes to slide down a perfectly smooth $45{^\circ}$ 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) $\sqrt{\frac{1}{1 - n^{2}}}$
Explanation
(a) $\mu = \tan\theta\left( 1 - \frac{1}{n^{2}} \right) = 1 - \frac{1}{n^{2}}\ \ \ \lbrack As\ \theta = 45{^\circ}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.