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A block of mass m is attached to a cart of mass 4 m through spring of spring constant k as shown in the figure. Friction is absent everywhere. The time period of oscillations of the system, when spring is compressed and then released, is

Options

  1. Aπ m k
  2. B2 π m k
  3. C2 π 5 m 2 k
  4. D4 π m 5 k

Correct answer

D. 4 π m 5 k

Step-by-step solution

It is equivalent to a system as shown below,   T = 2 π m reduced k ∴       T = 2 π m × 4 m 5 m k =    2 π 4 m 5 k    =    4 π m 5 k

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