Q: A particle of mass *m* is kept on a fixed, smooth sphere of radius R at a position where the radius through the particle makes an angle of 30° with the vertical. The particle is released from this position. The distance travelled by the particle before it leaves contact with the sphere is

(a) $ \displaystyle R (\theta + \pi/6) ; \theta = cos^-1 \frac{1}{\sqrt3}$

(b) $ \displaystyle R (\theta – \pi/6) ; \theta = cos^-1 \frac{1}{\sqrt3}$

(c) $ \displaystyle R (\theta/2 + \pi/6) ; \theta = cos^-1 \frac{1}{\sqrt3}$

(d) $\displaystyle R (\theta/2 – \pi/6) ; \theta = cos^-1 \frac{1}{\sqrt3}$

Ans: (b)