A meter stick connected with disc of same mass which is joined at one end of stick and disc can freely rotate about its joint. System swings in a vertical plane about a fixed horizontal axis passing t

Question

A meter stick connected with disc of same mass which is joined at one end of stick and disc can freely rotate about its joint. System swings in a vertical plane about a fixed horizontal axis passing through its one end, undergoes small oscillation of frequency $f_{0}$ . If disc is removed from the stick, then its new frequency of small oscillation is $\frac{4}{k} f_{0}$ . Find the value of k.

TestHub · Accepted Answer

With disc: I 0 ​ = 3 m ℓ 2 ​ + m ℓ 2 = 3 4 m ℓ 2 ​ , d = 4 3 ℓ ​ , M = 2m, so f 0 ​ = 2 π 1 ​ 4 m ℓ 2 /3 2 m g ⋅ 3 ℓ /4 ​ ​ = 2 π 1 ​ 8 ℓ 9 g ​ ​ . Without disc: I = 3 m ℓ 2 ​ , d = 2 ℓ ​ , so f = 2 π 1 ​ m ℓ 2 /3 m g ℓ /2 ​ ​ = 2 π 1 ​ 2 ℓ 3 g ​ ​ . f 0 ​ f ​ = 9 g /8 ℓ 3 g /2 ℓ ​ ​ = 3 4 ​ ​ = k 4 ​ ​ ⇒ k = 3 . Answer: 3.

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