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JIPMER 2018
Exam
JIPMER
Year
2018
Subject
Physics
Chapter
Oscillations

JIPMER 2018 · Physics · Oscillations

A particle doing SHM having amplitude 5 cm , mass 0.5 kg and...

A particle doing SHM having amplitude 5 cm , mass 0.5 kg and angular frequency 5rad/s5 \mathrm{rad} / \mathrm{s} is at 1 cm from mean position. Find potential energy and kinetic energy.

Options

  1. AKE=6.25×10−4 J,PE=150×10−3 J\mathrm{KE}=6.25 \times 10^{-4} \mathrm{~J}, \mathrm{PE}=150 \times 10^{-3} \mathrm{~J}
  2. BKE=150×10−4 J,PE=6.25×10−4 J\mathrm{KE}=150 \times 10^{-4} \mathrm{~J}, \mathrm{PE}=6.25 \times 10^{-4} \mathrm{~J}
  3. CKE=6.25×10−4 J,PE=6.25×10−4 J\mathrm{KE}=6.25 \times 10^{-4} \mathrm{~J}, \mathrm{PE}=6.25 \times 10^{-4} \mathrm{~J}
  4. DKE=150×10−3 J,PE=150×10−4 J\mathrm{KE}=150 \times 10^{-3} \mathrm{~J}, \mathrm{PE}=150 \times 10^{-4} \mathrm{~J}

Correct answer

B. KE=150×10−4 J,PE=6.25×10−4 J\mathrm{KE}=150 \times 10^{-4} \mathrm{~J}, \mathrm{PE}=6.25 \times 10^{-4} \mathrm{~J}

Step-by-step solution

Given, m=0.5 kg.ω=5rad/s,x=10−2 m\mathrm{m}=0.5 \mathrm{~kg} . \omega=5 \mathrm{rad} / \mathrm{s}, \mathrm{x}=10^{-2} \mathrm{~m},A=5×10−2 m\mathrm{A}=5 \times 10^{-2} \mathrm{~m} ∵\because Potential energy, U=12 mω2x2\mathrm{U}=\frac{1}{2} \mathrm{~m} \omega^2 \mathrm{x}^2 or U=12×0.5×(5)2×(10−2)2\quad \mathrm{U}=\frac{1}{2} \times 0.5 \times(5)^2 \times\left(10^{-2}\right)^2 =254×10−4 J=6.25×10−4 J=\frac{25}{4} \times 10^{-4} \mathrm{~J}=6.25 \times 10^{-4} \mathrm{~J} ∵\because Kinetic energy, K=12 mω2( A2−x2)\mathrm{K}=\frac{1}{2} \mathrm{~m} \omega^2\left(\mathrm{~A}^2-\mathrm{x}^2\right) or K=12×0.5×(5)2(25−1)×10−4\mathrm{K}=\frac{1}{2} \times 0.5 \times(5)^2(25-1) \times 10^{-4} =150×10−4 J=150 \times 10^{-4} \mathrm{~J}
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