A light spring is suspended with mass m_1 at its lower end and it… - Vidyadip

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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