Question

A small mass $m$ starts from rest and slides down the smooth spherical surface of Radius $R$. Assume zero potential energy at the top. Find the speed of the mass as a function of the angle $\theta$ made by the radius through the mass with the vertical.

• A. $v=\sqrt{2gR(1+\cos \theta )}$
• B. $v=\sqrt{2gR(1-\cos \theta )}$
• C. $v=\sqrt{2gR\cos \theta }$
• D. $v=\sqrt{2gR(1-\sin \theta )}$

Answer 1

The correct option is B $v=\sqrt{2gR(1-\cos \theta )}$

Loss in potential energy is converted into the kinetic energy,
$\frac{1}{2}m{v}^2=mgR(1-\cos \theta )$
$v=\sqrt{2gR(1-\cos \theta )}$