Question

A small particle of mass $m$ is released from rest from point $A$ inside a smooth hemispherical bowl as shown in the figure. The ratio $(x)$ of magnitude of centripetal force and normal reaction on the particle at any point $B$ varies with $\theta$ as

• A. (a)
• B.
• C.
• D.

Answer 1

Answer: (A)

$\because h=R \sin \theta$

$\therefore $ Speed of the particle at point $B$,
$v^{2}=2 g h=2 R g \sin \theta$
Centripetal force, $F=\frac{m v^{2}}{R}=2 m g \sin \theta\,\,\,...(i)$
Equation of motion gives
$N-m g \sin \theta=\frac{m v^{2}}{R}=2 m g \sin \theta$