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 $5T/3$. Then the ratio of $m/M$ is
AIEEE 2003,AIIMS 2016, Medium
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(d) $T \propto \sqrt m $
==> $\frac{{{T_2}}}{{{T_1}}} = \sqrt {\frac{{{m_2}}}{{{m_1}}}} $
==> $\frac{5}{3} = \sqrt {\frac{{M + m}}{M}} $
==> $\frac{{25}}{9} = \frac{{M + m}}{M}$
==> $\frac{m}{M} = \frac{{16}}{9}$
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