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A disc of mass m is attached to a spring of stiffness k as shown in the fig. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is
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1 √k / m 2π
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1 √2k / m 2π
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1 √2k / 3m 2π
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1 √3k / 2m 2π
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Correct Option: C
Taking moments about instantaneous centre ‘A’, Iaθ̇̇ + (kx) r = 0
⇒ (Io + mr2) θ̇̇ + kx (θr)r = 0
| ⇒ |  | mr2 + mr2 |  | θ | + k(θr2) = 0 | |
| 2 |
| ⇒ θ̇̇ + | θ = 0 | |
| 2 |
| ⇒ θ̇̇ + | θ = 0 | |
| 3m |
| ∴ ωn = | √2k / 3m | |
| 2π |
