Question

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

A
17.7 m/s
B
10.2 m/s
C
12.4 m/s
D
16.0 m/s

Solution

## The correct option is B $$17.7\ m/s$$To complete the circle, $$\displaystyle\dfrac{m\,v_0^2}{R} = mg\Rightarrow v_0^2 = g\,R$$Now, from conservation of energy:$$K_1+\cup_1=K_2+\cup_2$$$$\displaystyle\dfrac{1}{2}mv^2+0=\displaystyle\dfrac{1}{2}mv_0^2+mg\;(2R)$$$$\Rightarrow v^2=g\,R+4g\,R\Rightarrow v=\sqrt{5g\,R}$$$$\Rightarrow v=\sqrt{5\times10\times6.4} = 17.7\;m/s$$Physics

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