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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
Abody performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is
  • A
    $\frac{\sqrt{3} R}{2}$
  • B
    $\frac{R}{\sqrt{2}}$
  • ✓
    $\sqrt{3} R$
  • D
    $\sqrt{2} R$
✓

Answer

Correct option: C.
$\sqrt{3} R$
c
$\frac{1}{2} k\left(A^{2}-x^{2}\right)=\frac{1}{4}\left(\frac{1}{2} k A^{2}\right)$

$\therefore x=\frac{\sqrt{3}}{2} A$

$\therefore C D=C B=\frac{\sqrt{3}}{2} R$

or $B D=2(C D)$

or $2(C B)=\sqrt{3} R$

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