Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s - 1 , and amplitude 1 . 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s - 2 ).

Question

Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad s - 1 , and amplitude 1 . 6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 m s - 2 )., 20 N, 60 N, 40 N, 10 N

MARKS App · Accepted Answer

Given ω = 2 5 rad/s and A = 1.6 cm ∴ ω = k m = 2 5 ⇒ k = 25 2 Maximum compression in the spring = x o + A = mg k + A = 1 × 1 0 × 1 0 0 2 5 × 2 5 + 1.6 cm = 8 5 + 1.6 = 1.6 + 1.6 = 3.2 cm ∴ F m a x = 4 g + K ( x + A ) = 40 + 20 = 60 N

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