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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. Then the value of x is:

Asked in NEET 2024 · Time period, length and g

• (1) √3
• (2) √2
• (3) 2√3
• (4) 4

Step-by-step solution

Why the other options are wrong

• (1) x=√3 would mean T'=(√3)/2T≈ 0.87 T; halving the length can only give T'=T/√2≈ 0.71 T, and no reading of the data produces the factor 0.87
• (3) comes from using the spring formula T=2π√m/k, in which the mass does matter: T'=√3 T gives x/2=√3 and x=2√3, and the length change has been ignored
• (4) comes from taking T∝1/ℓ rather than T∝√ℓ, so that halving the length doubles the period: x/2=2 and x=4

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