Question

In a "well of death", a person rides on the vertical face of a cylinder. The coefficient of friction between the tyres and the surface is ${}^{\prime }{\mu }^{\prime }$. Find the minimum velocity with which he should ride for him not to fall.

• A. $\frac{gr}{\mu }$
• B. $\sqrt{\frac{gr}{\mu }}$
• C. $\sqrt{\frac{2gr}{\mu }}$
• D. $\sqrt{\frac{gr}{2\mu }}$

Answer 1

The correct option is B $\sqrt{\frac{gr}{\mu }}$

By the free body diagram,
Here, for condition of the rider not to fall, the normal force should provide necessary centripetal force:
$\Rightarrow$$N=\frac{m{v}^2}{r}$

Balancing the vertical forces we get,
$f_{\text{max}}=\mu N=\frac{\mu m{v}^2}{r}$
For him not to fall;
$f_{\text{max}}\ge mg\Rightarrow \frac{\mu m{v}^2}{r}\ge mg$
$\Rightarrow v\ge \sqrt{\frac{gr}{\mu }}$
$\therefore v_{\text{min}}=\sqrt{\frac{gr}{\mu }}$

Option B is the correct answer.