JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Elasticity & SHM

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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

\frac{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) $2 T \frac{1}{10}$
(B) $2 T \frac{1}{14}$
(C) $4 T \frac{1}{15}$ ✓ Correct
(D) $4 T \frac{1}{14}$

Answer: (C)

Solution

When the bob is submerged, buoyancy trims the effective gravity to

g_{e f f} = g (1 - \frac{ρ _{l i q u i d}}{ρ _{b o b}}) = g (1 - \frac{1}{16}) = \frac{15 g}{16}

. Since

T \propto \frac{1}{g _{e f f}}

, the new period is

T^{'} = T \frac{g}{g _{e f f}} = T \frac{16}{15} = \frac{4 T}{15} = 4 T \frac{1}{15}

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option

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