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Most Important Selected Qs for JEE AdvancedPhysicsOscillations

A long thin uniform rod of length L and mass m is free to rotate in a vertical plane about a horizontal fixed axis through its one end "O". A light spring of force constant k is connected vertically between the other end A of the rod and ground. When the rod is in equilibrium, it is parallel to the ground.

Options

  1. AThe period of small oscillations when the rod is rotated slightly and released is 2 m 3 k
  2. BThe period of small oscillations when the rod is rotated slightly and released is 2 m k
  3. CThe maximum speed of the displaced end of the rod is L ₀ 3 k m (The angular amplitude of small oscillations I
  4. DThe maximum speed of the displaced end of the rod is L ₀ 3 k m (The angular amplitude of small oscillations is

Correct answer

C. The maximum speed of the displaced end of the rod is L ₀ 3 k m (The angular amplitude of small oscillations I

Step-by-step solution

(a) Restoring torque about "O" due to elastic force of the spring, aligned & =-F L=-k y L(F=k y) & =-k L^2 ( as y=L ) aligned aligned & =l = 1 3 M L^2 d^2 d t^2 & 1 3 M L^2 d^2 d t^2 =-k L^2 & d^2 d t^2 =- 3 k M or = 3 k M and T=2 M 3 K aligned (b) In angular SHM, maximum angular velocity aligned & ( d d t )_ = ₀ = ₀ 3 k M & v=r(d / d t) aligned So, v_ =L ( d d t )_ =L ₀ 3 k M

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