Question

A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little then released, so that the mass executes simple harmonic motion of time period $T.$ If the mass is increased by $m,$ the time period becomes $\frac{5T}{3}$. The ratio of $\frac{m}{M}$ is:

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

Answer 1

The correct option is C $\frac{16}{9}$

$T=2\pi \sqrt{\frac{M}{k}}$
$\frac{5T}{3}=2\pi \sqrt{\frac{M+m}{k}}$
Solving these two equations, we get
$\frac{m}{M}=\frac{16}{9}$