Question

A small mass $m$ starts sliding down a smooth and stationary semi-circular track. Which of the following graph best represents the variation of the magnitude of the force applied by the track on the mass and the angle $\theta$ ? ( assume initially $\theta =0$)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B



By energy conservation, we have
$\frac{1}{2}m{v}^2=mgRsin\theta \text{From Newtons laws of motion and Free Body Diagram}\Rightarrow \frac{m{v}^2}{R}=N-mgsin\theta N=\frac{m{v}^2}{R}+mgsin\theta N=3mgsin\theta$