A body of mass m is attached to the lower end of a spring whose other 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 mass m is increased by 1 kg, the time period becomes 5 s. The value of m in kg is:
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Question

A body of mass m is attached to the lower end of a spring whose other 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 mass m is increased by 1 kg, the time period becomes 5 s. The value of m in kg is:

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G1 Physics · Accepted Answer

Step 1: For the same spring constant, T = 2π√(m/k), so T² ∝ m. Step 2: Initially T₁ = 3 s for mass m, and T₂ = 5 s for mass m + 1 kg. Step 3: (T₂/T₁)² = (m + 1)/m = 25/9. Step 4: 25m = 9m + 9, giving 16m = 9. Step 5: Hence m = 9/16 kg. Final answer: (D) 9/16.