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

Answer 1

The correct option is C

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

Acceleration of body along AB is $gcos\theta$
Distance travelled in time t sec = AB = $\frac{1}{2}\left(gcos\theta \right)t^2$
From $\Delta ABC,AB=2Rcos\theta ;2Rcos\theta =\frac{1}{2}gcos\theta t^2$
$\Rightarrow t^2=\frac{4R}{g}ort=2\sqrt{\frac{R}{g}}$