Two point masses m 1 and m 2 are fixed to a light rod hinged at one end. The masses are at distances λ 1 and λ 2 respectively from the hinge. Find the time period of oscillation (small amplitude) of this system in seconds if m 1 = m 2 , λ 1 = 1m, λ 2 = 3m.
Text Solution
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π
Sol.
Net restoring torque about O
= m 1 g λ 1 sinθ + m 2 g λ 2 sinθ = (m 1 λ 1 + m 2 λ 2 )g sinθ
for small oscillation sinθ ~ θ
⇒ τ restoring = (m 1 λ 1 + m 2 λ 2 )gθ
compare with τ = Cθ
C = (m 1 λ 1 + m 2 λ 2 )g
= π
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