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

• Correct answer
  A

  
  
• B

  
  
• C

  
  
• D

  
  

Solution

$\because \quad h=R \sin \theta$
$\therefore$ 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 $N-m g \sin \theta=\frac{m v^2}{R}=2 m g \sin \theta$

Hence, the correct answer is option: 'A'.