Question

A biker is performing stunt in a cylindrical death well of radius $16\text{m}$. If speed of biker is constant and coefficient of friction of well's surface is $0.2$, find the minimum speed required to perform the stunt safely.

• A. $24\text{m/s}$
• B. $28\text{m/s}$
• C. $16\text{m/s}$
• D. $49\text{m/s}$

Answer 1

The correct option is B $28\text{m/s}$


We know for uniform circular motion
Centripetal acceleration, $a_C=\frac{m{v}^2}{r}$

From FBD,
Along $x-$ axis,
$N=\frac{m{v}^2}{r}$
Along $y-$ axis,
$f=mg$
We know that,
Frictional force, $f=\mu N$
$\therefore mg=\mu \left(\frac{m{v}^2}{r}\right)$
$\Rightarrow v=\sqrt{\frac{rg}{\mu }}$
$=\sqrt{\frac{16\times 9.8}{0.2}}$
$=28\text{m/s}$
Minimum speed of biker should be $28\text{m/s}$ such that friction will be sufficient to balance weight in $y-$ direction.