A particle of mass m is suspended at the lower end of a thin rod of negligible mass. The upper end of the rod is free to rotate in the plane of the page about a horizontal axis passing through the point O. The spring is undeformed when the rod is vertical as shown in fig. If the period of oscillation of the system is 
, when it is slightly displaced from its mean position then find n. Take k = 
and g = 10m/s 2 .
Text Solution
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When the small angular displacement Given to rod
for small displacement
x = λ sin θ
kx = k λ sin θ
Torque about point O = Ι o α
(kx) λ + mg sin θ λ = mL 2 α
α = 
For small θ
α = 
Time period T = 2 π 
= 
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