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’, time period becomes $\large \frac{{5T}}{3}$ , then the ratio of (m / M ) is

Easy

A

$\large \frac{3}{2}$
B

$\large \frac{{25}}{9}$
C

$\large \frac{{16}}{9}$
D

$\large \frac{5}{3}$

Solution

$\large T\, = \,2\pi \sqrt {\frac{M}{k}} \,\, \Rightarrow {T^1}\, = \,2\pi \sqrt {\frac{{M + m}}{k}}$
$\large \frac{{{T^1}}}{T}\, = \,\sqrt {\frac{{M + m}}{M}} \, \Rightarrow \frac{5}{3}\, = \,\sqrt {\frac{{M + m}}{M}}$
25 M = 9 M + 9 m $\large \Rightarrow$ 16M = 9m
$\large \frac{{16}}{9}\, = \,\frac{m}{M}$

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