First slide

Simple hormonic motion

Question

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of time period T. If the mass is increased by m, the time period becomes $\frac{5 T}{3}$ . Then the ratio of $\frac{m}{M} is$

Moderate

A

$\frac{5}{3}$
B

$\frac{3}{5}$
C

$\frac{25}{9}$
D

$\frac{16}{9}$

Solution

$T \propto \sqrt{m} \Rightarrow \frac{T_{2}}{T_{1}} = \sqrt{\frac{m_{2}}{m_{1}}} \Rightarrow \frac{5}{3} = \sqrt{\frac{M + m}{M}}$
$\Rightarrow \frac{25}{9} = \frac{M + m}{M} \Rightarrow \frac{m}{M} = \frac{16}{9}$

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