A mass M is suspended from a spring of negligible mass. spring is pulled a little and then released

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13.Oscillations

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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

A

$\frac{5}{3}$

B

$\frac{3}{5}$

C

$\frac{{25}}{9}$

D

$\frac{{16}}{9}$

(AIEEE-2003) (AIIMS-2016)

Solution

(d) $T \propto \sqrt m $

==> $\frac{{{T_2}}}{{{T_1}}} = \sqrt {\frac{{{m_2}}}{{{m_1}}}} $

==> $\frac{5}{3} = \sqrt {\frac{{M + m}}{M}} $

==> $\frac{{25}}{9} = \frac{{M + m}}{M}$

==> $\frac{m}{M} = \frac{{16}}{9}$

Standard 11

Physics

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