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Oscillations — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsOscillations1 Mark
MCQ
A light spring is suspended with mass $m_1$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $T$ second. When a mass $m_2$ is added to $m_1$ and the system is made to oscillate, the period is found to be $\frac{3}{2} T$. The ratio of $m_1: m_2$ is
  • A
    $2: 3$
  • B
    $3: 4$
  • ✓
    $4: 5$
  • D
    $5: 6$
✓

Answer

Correct option: C.
$4: 5$
As, $T=2 \pi \sqrt{\frac{m}{K}}$$T=2 \pi \sqrt{\frac{m_1}{K}} \ldots \text { (i) } ;$
$\frac{3 T}{2}=2 \pi \sqrt{\frac{m_1+m_2}{K}} \ldots \text { (ii) }$
Divide equation $(i)$ by equation $(ii)$
$ \frac{2}{3}=\sqrt{\frac{m_1}{m_1+m_2}} ;$
$\frac{4}{9}=\frac{m_1}{m_1+m_2}$
$4 _1+4 m_2=9 m_1$
$4 m_2=5 m_1$
$m_1: m_2=4: 5$

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