A mass M is suspended from a spring of negligible mass. The spring...

A mass

\mathrm{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

\mathrm{m}

, the time period becomes

\frac{5 \mathrm{~T}}{3}

. Then the ratio of

\frac{\mathrm{m}}{\mathrm{M}}

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

Options

A $\frac{3}{5}$
B $\frac{25}{9}$
C $\frac{16}{9}$
D $\frac{5}{3}$

Correct answer

C. $\frac{16}{9}$

Step-by-step solution

\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K}}}

\frac{5 \mathrm{~T}}{3}=2 \pi \sqrt{\frac{\mathrm{M}+\mathrm{m}}{\mathrm{K}}}

Dividing equation (ii) by equation (i),

\frac{5}{3}=\sqrt{\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}}

. Squaring both the sides

\frac{25}{9}=\frac{M+m}{M}=1+\frac{m}{M} \Rightarrow \frac{m}{M}=\frac{25}{9}-1=\frac{16}{9}

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