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.
• B.
• C.
• D.

Answer 1

The correct option is C

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