Question
Point mass slides from rest from the topmost point of vertical circle of radius r along the smooth chord. Show that the time of descend of mass along the chord is independent of chord chosen.
Solution
Given,
Radius of the circle = r
Consider, an arbitrary chord AB which subtends an angle 
with vertical.
Now, the length of chord AB is given by,
Acceleration of mass along inclined plane is, 
Now, using the equation of motions,
∴ 
Since t is independent of 
, hence time of descend of mass is independent of the choice of chord.
