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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches at distance $4 \,cm$ from mean position, it is stopped for a moment and then released. The new energy of vibration will be ........... $J$
  • ✓
    $40$
  • B
    $50$
  • C
    $90$
  • D
    $60$
✓

Answer

Correct option: A.
$40$
a
(a)

Energy $=90 \,J \quad$ Amplitude $=6 \,cm$

Maximum energy $=\frac{1}{2} m A^2 \omega^2=90$

$\text { or } m \omega^2=\frac{180}{36 \times 10^{-4}}$

$\therefore m \omega^2=30 \times 10^2$

When particle is stopped the point where it is stopped is the new amplitude but angular velocity will remain same.

$E=\frac{1}{2} m A_2^2 \omega^2$

$\text { or } E=3000 A_2^2$

$A_2=4 \times 10^{-2}$

$A_2=3000$

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