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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Physics
Chapter
Oscillations

JEE Main 2004 · Physics · Oscillations

The bob of a simple pendulum executes simple harmonic motion in...

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 tandt0t and t_0 is true?

Options

  1. At=t0t=t_0
  2. Bt=t0/2t=t_0 / 2
  3. Ct=2t0t=2 t_0
  4. Dt=4t0\mathrm{t}=4 \mathrm{t}_0

Correct answer

C. t=2t0t=2 t_0

Step-by-step solution

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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