Question

A motorcyclist wants to drive on the vertical surface of a wooden well of radius $5m$, with a minimum speed of $5\sqrt{5}$. The minimum value of coefficient of friction between the tyres and the wall of the wood must be:

• A. $0.10$
• B. $0.20$
• C. $0.30$
• D. $0.40$

Answer 1

The correct option is D $0.40$

Given: a motorcyclist wants to drive on the vertical surface of a wooden well of radius 5m, with a minimum speed of $5\sqrt{5}$

To find the minimum value of coefficient of friction between the tyres and the wall of the wood

Solution:

Friction force, $f=mg$

Centripetal force, $N=\frac{m{V}^2}{r}$

Hence,

$\mu =\frac{f}{N}⟹\mu =\frac{mg}{\frac{m{V}^2}{r}}⟹\mu =\frac{rg}{V^2}⟹\mu =\frac{5\times 10}{(5\sqrt{5}{)}^2}⟹\mu =0.4$

is the minimum value of coefficient of friction between the tyres and the wall of the wood