Question

A hollow sphere has radius $6.4m$. Minimum velocity required by a motor cyclist at bottom to complete the circle will be

• A. $17.7m/s$
• B. $10.2m/s$
• C. $12.4m/s$
• D. $16.0m/s$

Answer 1

Answer: (A)

$17.7m/s$

To complete the circle, $\frac{m{v}_0^2}{R}=mg\Rightarrow v_0^2=gR$
Now, from conservation of energy:
$K_1+{\cup }_1=K_2+{\cup }_2$

$\frac{1}{2}m{v}^2+0=\frac{1}{2}m{v}_0^2+mg\left(2R\right)$

$\Rightarrow v^2=gR+4gR\Rightarrow v=\sqrt{5gR}$

$\Rightarrow v=\sqrt{5\times 10\times 6.4}=17.7m/s$