Question

1. A particle slides from rest from the topmost point of a
vertical circle of radius r along a smooth chord making
an angle with the vertical. The time of descent is
(a) Least for 0=0 (b) Maximum for 0 = 0
(c) Least for 0= 45° (d) Independent of e
1 A body is the nortinn1.n ords from A​

Answer 1

Given that,

Radius = r

Angle = θ

We know that,

The force on particle along the chord is

$F= mg\cos\theta$

The distance travelled by the particle is $\dfrac{d}{\cos\theta}$

Where, d = diameter of the circle

We need to calculate the time of descent

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

Here, u = o

So, $s=\dfrac{at^2}{2}$

$t=\sqrt{\dfrac{2s}{a}}$

Hence, t is independent of θ.

(d) is correct option.