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. $\frac{\sqrt{2gR}}{g\,cos\,\theta}$
• 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)

Acceleration of body along $AB$ is $g cos \theta$. Distance travelled in time $t$ sec is
$AB =\frac{1}{2}$ $(g cos \theta)t^2$

From $\Delta;ABC, AB = 2R cos \theta$
Thus, $2 R cos \theta \frac{1}{2} g cos \theta t^2$
$\Rightarrow t^{2}=\frac{4\,R}{g} \Rightarrow t=2\sqrt{\frac{R}{g}}$