If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x/2 times its original time period. The value of x is:
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Question

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x/2 times its original time period. The value of x is:

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G1 Physics · Accepted Answer

Step 1: A simple pendulum has period T = 2π√(L/g), which does not depend on bob mass. Step 2: After the changes, L′ = L/2, so T′ = 2π√(L/(2g)) = T/√2. Step 3: Compare T′/T = 1/√2 = x/2. Step 4: Therefore x = 2/√2 = √2. Final answer: (A) √2.