A solid cylinder is attached to a horizontal massless spring as shown in figure. If the cylinder rolls without slipping, the time period of oscillation of the cylinder is

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Let x be the extension in the spring, Then, x = 2 Rθ ∴ Torque acting on the cylinder about point of contact, T = F × 2 R = − K x ( 2 R ) = − 4 R 2 K ⋅ θ ∴ T = 2 π Ke I ​ ​ = 2 π 4 R 2 K 2 3 ​ M R 2 ​ ​ = 2 π 8 K 3 M ​ ​

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