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JEE Advanced2009PhysicsOscillationsActual

A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k . The springs are fixed to rigid supports as shown in the figure, and rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle in one direction and released. The frequency of oscillation is

Options

  1. A1 2 2 k M
  2. B1 2 k M
  3. C1 2 6 k M
  4. D1 2 24 k M

Correct answer

C. 1 2 6 k M

Step-by-step solution

aligned & Restoring torque =-(2 k x) L 2 & =- k L(L / 2 ) I =- [ k L^2 / 2 M L^2 / 12 ] aligned aligned & =- ( 6 k M ) f & = 1 2 | | = 1 2 6 k M aligned

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