Question:
A simple pendulum oscillating in air has period \(T\). The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :
A simple pendulum oscillating in air has period \(T\). The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :
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Buoyancy reduces the effective gravity: \(g_{eff}=g\left(1-\frac{\rho_{liquid}}{\rho_{bob}}\right)\).
Updated On: Nov 5, 2026
- \(2T\sqrt{\frac{1}{10}}\)
- \(4T\sqrt{\frac{1}{14}}\)
- \(4T\sqrt{\frac{1}{15}}\)
- \(2T\sqrt{\frac{1}{14}}\)
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The Correct Option is C
Solution and Explanation
Weight of bob \(=V\rho g\); buoyant force \(=V\frac{\rho}{16}g\) upward.
Net downward force \(=V\rho g\left(1-\frac1{16}\right)\), so \(g_{eff}=\frac{15}{16}g\).
\(T=2\pi\sqrt{\frac{L}{g}}\Rightarrow T'=2\pi\sqrt{\frac{L}{g_{eff}}}=T\sqrt{\frac{16}{15}}=4T\sqrt{\frac{1}{15}}\).
Answer: (3) \(4T\sqrt{\frac{1}{15}}\)
Net downward force \(=V\rho g\left(1-\frac1{16}\right)\), so \(g_{eff}=\frac{15}{16}g\).
\(T=2\pi\sqrt{\frac{L}{g}}\Rightarrow T'=2\pi\sqrt{\frac{L}{g_{eff}}}=T\sqrt{\frac{16}{15}}=4T\sqrt{\frac{1}{15}}\).
Answer: (3) \(4T\sqrt{\frac{1}{15}}\)
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