Question

A body slides down a rough plane inclined to the horizontal at ${30}^0$. If $70\%$ of the initial potential energy is dissipated during the descent, the coefficient of sliding friction is:

• A. $0.7$
• B. $\sqrt{\frac{0.7}{2}}$
• C. $\frac{0.7}{\sqrt{3}}$
• D. $\frac{0.7}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{0.7}{\sqrt{3}}$

Friction force is $\mu mgcos\theta ,\theta ={30}^o$

Let $h$ be the height.

Energy dissipated is: $E_f=\mu mgcos\theta \times \frac{h}{\sin \theta }$

$PE=mgh$

Now, $\frac{E_f}{PE}=0.7$

So, $\mu cot\theta =0.7$

So, $\mu =\frac{0.7}{\sqrt{3}}$