Question

A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

• A. $\frac{2\sqrt{gR}}{g\cos\theta}$
• B. $2\sqrt{gR}.\frac{\cos\theta}{g}$
• C. $2\sqrt{\frac{R}{g}}$
• D. $\frac{gR}{\sqrt{g\cos\theta}}$

Answer 1

Answer: (C)

$2\sqrt{\frac{R}{g}}$

Answer 2

Acceleration of body along AB is $g\cos\theta$

Distance travelled in time t sec =$AB = \frac{1}{2}(g\cos\theta)t^{2}$

From$\Delta ABC,\mspace{6mu} AB = 2R\cos\theta;\mspace{6mu} 2R\cos\theta = \frac{1}{2}g\cos\theta t^{2}$

⇒ $t^{2} = \frac{4R}{g}$or $t = 2\sqrt{\frac{R}{g}}$