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A body of mass, m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3   s . When the mass m is increased by 1   kg , the time period of oscillations becomes 5   s . The value of m in kg is

Options

  1. A3 4
  2. B4 3
  3. C16 9
  4. D9 16

Correct answer

D. 9 16

Step-by-step solution

T 1 = 3 = 2 π m K . Then, T 2 = 5 = 2 π m + 1 K . By dividing both the equations, we get, 3 5 = m m + 1 9 25 = m m + 1 9 m + 9 = 25   m 16 m = 9 m = 9 16 .

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