SHMHard
Question
A system of two identical rods (L - shaped) of mass m and length 2L are resting on a peg P as shown in the figure. If the system is displaced in its plane by a small angle, find the period of oscillations
Options
A.
B.
C.
D.
Solution
Center of mass 2 m of a system is at a distance from peg P is 
and moment of inertia of the system is 
τ = r × F = - mg sin θ
⇒ Iα = - mg sin (in θ = θ for small θ)
⇒ α = - mgθ ⇒ α = - 
= - ω2θ
⇒ ω =
and moment of inertia of the system is τ = r × F = - mg sin θ
⇒ Iα = - mg sin
(in θ = θ for small θ)⇒
α = - mgθ ⇒ α = - = - ω2θ⇒ ω =
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