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 SHM 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 :

Easy

A

$\frac{3}{5}$
B

$\frac{25}{9}$
C

$\frac{16}{9}$
D

$\frac{5}{3}$

Solution

$T \propto \sqrt{M} \Rightarrow \frac{3}{T} = \sqrt{\frac{M + m}{M}} \Rightarrow \frac{25}{9} = \frac{M + m}{M} \Rightarrow \frac{m}{M} = \frac{16}{9}$

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