A ball is hung vertically by a thread of length '' from a point 'P' of an inclined wall that makes an angle 'α' with the vertical. The thread with the ball is then deviated through a small angle 'β' (β > α) and set free. Assuming the wall to be perfectly elastic, the period of such pendulum is/are
Text Solution
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(b, d)
max m amplitude = β λ
So time to travel angle α
x = x 0 sin ꞷt
α λ = β λ sin ꞷt
t = 
sin –1 
Now period of pendulum = 
(actual time period) +2 (time to travel angle α)
= 
. 2 π 
+ 2 
sin –1 
= 2 
Also if time taken to travel from right extreme position to wall is t then
– α = β cos ꞷt
⇒ cosꞷt = – 
t = 
T = 2t = 
T = 
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