If time period of small oscillation for given system about its mean position is given as $T = 2 π \frac{β m}{γ k}$ then fill value of $\frac{3 γ}{2 β}$ where $β$ and $γ$ are least possible integer. Disc always rolls purely.

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TestHub · Accepted Answer

τ = − k ( Rθ ) R − k ( 2 Rθ ) ( 2 R ) τ = − 5 k R 2 θ I contact ​ = 2 3 ​ m R 2 θ ¨ + 3 m 10 k ​ θ = 0 ω 2 = 3 m 10 k ​ T = 2 π 10 k 3 m ​ ​ β = 3 , γ = 10 2 β 3 γ ​ = 6 30 ​ = 5 ​

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