Question

A particle slides from rest from the topmost point of a vertical circle of radius ($r$) along a smooth chord making an angle $\left(\theta \right)$ with the vertical the time of decent is

• A. Least for $\theta =0^{\circ }$
• B. Maximum for $\theta =0^{\circ }$
• C. Least for $\theta ={45}^{\circ }$
• D. Independent of $\theta$

Answer 1

The correct option is D Independent of $\theta$

Force on particle along the cord = $mg\cos \theta$

Distance travelled by the particle =$\frac{d}{\cos \theta }$, where $d$ is the diameter or the vertical circle.

$s=\frac{a{t}^2}{2}$

$\Rightarrow t=\sqrt{\frac{2s}{a}}$.

Hence,$t$ is independent of $\theta$.