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Time period of a spring-mass system is T . If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part, the new time period will be

Options

  1. A3 2 T
  2. BT 3
  3. C3 T 2
  4. D3 T

Correct answer

C. 3 T 2

Step-by-step solution

T = 2 π m k When spring is cut in the ratio 1 : 3, the force constant of the longer part is 4 k 3 . ∴    T' = 2 π 3 m 4 k = 3 2 T

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