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The following figure shows a block of mass m suspended from a fixed point by means of a vertical spring. The block is oscillating simple harmonically and carries a charge q . There also exists a uniform electric field in the region. Consider four different cases. The electric field is zero, in case-1, mg q downward in case-2, mg q upward in case- 3 and 2 mg q downward in case-4. The speed at mean position is same in

Options

  1. ATime periods of oscillation are equal in case-1 and case-3
  2. BAmplitudes of displacement are same in case-2 and case-3
  3. CThe maximum elongation (increment in length from natural length) is maximum in case-4
  4. DTime periods of oscillation are equal in case- 2 and case-4

Correct answer

D. Time periods of oscillation are equal in case- 2 and case-4

Step-by-step solution

(1) Only equilibrium position changes. Time period remains same T =2 ~m k . (2) 1 2 kx ^2= 1 2 mv ^2 v at mean position is same amplitude will be same. (3) In case -4 Eaquilibrium position x ₀= 3 mg k .

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