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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Oscillations

NEET 2009 · Physics · Oscillations

A simple pendulum performs simple harmonic motion about x=0 with an...

A simple pendulum performs simple harmonic motion about x=0\mathrm{x}=0 with an amplitude a and time period T. The speed of the pendulum at x=a/2\mathrm{x}=\mathrm{a} / 2 will be :

Options

  1. Aπa3 T\frac{\pi \mathrm{a} \sqrt{3}}{\mathrm{~T}}
  2. Bπa32 T\frac{\pi \mathrm{a} \sqrt{3}}{2 \mathrm{~T}}
  3. CπaT\frac{\pi a}{T}
  4. D3π2aT\frac{3 \pi^2 a}{T}

Correct answer

A. πa3 T\frac{\pi \mathrm{a} \sqrt{3}}{\mathrm{~T}}

Step-by-step solution

v=ωA2−x2=2πTa2−a24=πa3 T\quad \mathrm{v}=\omega \sqrt{\mathrm{A}^2-\mathrm{x}^2}=\frac{2 \pi}{\mathrm{T}} \sqrt{\mathrm{a}^2-\frac{\mathrm{a}^2}{4}}=\frac{\pi \mathrm{a} \sqrt{3}}{\mathrm{~T}}
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