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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Physics
Chapter
Oscillations

BITSAT 2021 · Physics · Oscillations

In a simple pendulum of length I the bob is pulled aside from its...

In a simple pendulum of length I the bob is pulled aside from its equilibrium position through an angle θ\theta and then released. The bob passes through the equilibrium position with speed

Options

  1. A2gl(1+cos⁡θ)\sqrt{2 g l(1+\cos \theta)}
  2. B2glsin⁡θ\sqrt{2 g l \sin \theta}
  3. C2gl\sqrt{2 \mathrm{ g} l}
  4. D2gl(1−cos⁡θ)\sqrt{2 \mathrm{ g} l(1-\cos \theta)}

Correct answer

D. 2gl(1−cos⁡θ)\sqrt{2 \mathrm{ g} l(1-\cos \theta)}

Step-by-step solution

If ll is length of pendulum and θ\theta be angular amplitude then from principle of conservation of energy (Initial total energy) 0+mgh=12mv2+00+\mathrm{mgh}=\frac{1}{2} m v^{2}+0 (Final total energy) ⇒v=2gh=2gl(1−cos⁡θ)\Rightarrow v=\sqrt{2 g h}=\sqrt{2 g l(1-\cos \theta)}
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