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NDA 1 2025 GAT, question 134

Topic: Physics

Q134

The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum ?

  1. (a) 3 : 1
  2. (b) 2 : 5
  3. (c) 2 : 1Correct answer
  4. (d) 3 : 2

Solution.

Answer: (c) 2 : 1

  1. For small oscillations, T=2πL/gT = 2\pi\sqrt{L/g}; the bob’s mass does not enter.
  2. With the new length 4L4L, Tnew/Told=4L/L=2T_{new}/T_{old} = \sqrt{4L/L} = 2.
  3. Hence the ratio is 2:12:1.