Question

An object takes $n$ times as much time as to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

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

Answer 1

Answer: (A)

The coefficient of kinetic friction between the object and the rough incline
$\mu =\tan \theta\left(1-\frac{1}{n^{2}}\right)$
$\mu =\tan 45^{\circ}\left(1-\frac{1}{n^{2}}\right)$
$=1-\frac{1}{n^{2}}$