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JIPMER 2014
Exam
JIPMER
Year
2014
Subject
Physics
Chapter
Oscillations

JIPMER 2014 · Physics · Oscillations

A mass of 1 kg is suspended from a spring of force constant 400 N ,...

A mass of 1 kg is suspended from a spring of force constant 400 N , executing SHM total energy of the body is 2 J , then maximum acceleration of the spring will be

Options

  1. A4 m/s24 \mathrm{~m} / \mathrm{s}^2
  2. B40 m/s240 \mathrm{~m} / \mathrm{s}^2
  3. C200 m/s2200 \mathrm{~m} / \mathrm{s}^2
  4. D400 m/s2400 \mathrm{~m} / \mathrm{s}^2

Correct answer

B. 40 m/s240 \mathrm{~m} / \mathrm{s}^2

Step-by-step solution

T=2πmR=2π1400=2π20T=2 \pi \sqrt{\frac{m}{R}}=2 \pi \sqrt{\frac{1}{400}}=\frac{2 \pi}{20} Frequency n=202πω=2πn=2π×202π=20n=\frac{20}{2 \pi} \omega=2 \pi n=2 \pi \times \frac{20}{2 \pi}=20 Total energy E=12mω2r2&2=12×1×400×r2\begin{aligned}& E=\frac{1}{2} m \omega^2 r^2 \& 2=\frac{1}{2} \times 1 \times 400 \times r^2\end{aligned}\begin{gathered}r=\frac{1}{10} \mathrm{ m} \\ \text{ Acceleration }=\omega^2 r=400 \times \frac{1}{10}=40 \mathrm{ m} / \mathrm{s}^2\end{gathered}$
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