Oscillations

JEE Main level, single correct, medium

143 of 194

Question 143 of 194

The bob of a simple pendulum executes simple harmonic motion in water with a period tt, while the period of oscillation of the bob is t0t_0 in air. Neglecting frictional force of water and given that the density of the bob is (43)×1000 kg/m3\left(\frac{4}{3}\right) \times 1000 \mathrm{~kg} / \mathrm{m}^3. What relationship between tt and t0t_0 is true?

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Answer: (C) t=2t0t=2 t_0

TT0=1(1−ρ′ρ)=11−13\frac{\mathrm{T}}{\mathrm{T}_0}=\sqrt{\frac{1}{\left(1-\frac{\rho^{\prime}}{\rho}\right)}}=\sqrt{\frac{1}{1-\frac{1}{3}}}
⇒TT0=2\Rightarrow \frac{\mathrm{T}}{\mathrm{T}_0}=2
or, T=2 T0\mathrm{T}=2 \mathrm{~T}_0

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