A metre stick swinging in vertical plane about an fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become :
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The new frequency will be 8 times the old frequency.
Explanation :
Conservation of angular momentum will hold true, i.e.
I₀f₀ = I₁f₁
old moment of inertia
I₀ = ML²/3
New mass , M₁ = M/2
New length, L₁ = L/2
Hence new moment of inertia
I₁ = M₁L₁²/3
= (M/2 x L²/4)/3
= ML²/24
Hence,
I₀f₀ = I₁f₁
=> ML²f₀/3 = ML²f₁/24
=> f₁ = 8f₀
Hence the new frequency will be 8 times the old frequency.
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