Question

A motorcyclist of mass $100\text{kg}$ is moving in a horizontal circle inside a hollow cylinder of radius $50\text{m}$. The coefficient of friction between the tires of the motorcycle and the surface of the hollow cylinder is $0.8$. Then, the minimum speed with which he should ride the motorcycle to keep moving in a horizontal circle is

• A. $25\text{m/s}$
• B. $0.5\text{m/s}$
• C. $50\text{m/s}$
• D. $2.5\text{m/s}$

Answer 1

The correct option is A $25\text{m/s}$

FBD of the motorcycle:

$N=mR{\omega }^2$... (1)
$f_s=mg$... (2)

From (1) and (2)
$\frac{f_s}{N}=\frac{g}{R{\omega }^2}$
Since $f_s\le {\mu }_{s}N$, we get ${\mu }_s\ge \frac{g}{R{\omega }^2}$
$\Rightarrow {\omega }^2\ge \frac{g}{\mu R}\Rightarrow {\omega }_{min}=\sqrt{\frac{g}{\mu R}}$
As $v=R\omega$,
$v_{min}=R\sqrt{\frac{g}{\mu R}}=\sqrt{\frac{gR}{\mu }}$
$=\sqrt{\frac{10\times 50}{0.8}}=25\text{m/s}$