Question

A person wants to drive on the vertical surface of a large cylindrical wooden well commonly known as death well in a circus. The radius of the well is $2$ meter, and the coefficient of friction between the tyres of the motorcycle and the wall of the well is $0.2$, the minimum speed of the motorcyclist must have in order to prevent slipping should be

• A. $15m/s$
• B. $10m/s$
• C. $25m/s$
• D. $20m/s$

Answer 1

The correct option is B $10m/s$

Given, radius of the circle, $r=2m$
And friction coefficient between tyre and wall of the well, $=0.2$
As the motorcyclist moves in the circle, the centripetal force is provided by the normal reaction. $N=\frac{m{v}^2}{r}\dots \left(i\right)$
To prevent slipping, $\mu N=mg$
Using equation $\left(i\right)$,
$\frac{\mu m{v}^2}{r}=mgv=\sqrt{\frac{rg}{\mu }}v=\sqrt{\frac{2\times 10}{0.2}}=10m/s$