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13. oscillations — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period
  • A
    $T = 2\pi \sqrt {\left( {mg/x(M + m)} \right)} $
  • ✓
    $T = 2\pi \sqrt {\left( {(M + m)x/mg} \right)} $
  • C
    $T = (\pi /2)\sqrt {\left( {mg/x(M + m)} \right)} $
  • D
    $T = 2\pi \sqrt {\left( {(M + m)/mgx} \right)} $
✓

Answer

Correct option: B.
$T = 2\pi \sqrt {\left( {(M + m)x/mg} \right)} $
b
(b) As $mg$ produces extension $x$, hence $k = \frac{{mg}}{x}$
 $T = 2\pi \sqrt {\frac{{(M + m)}}{k}} = 2\pi \sqrt {\frac{{(M + m)x}}{{mg}}} $

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