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, the time period becomes $\text{5T/3,}$ then the ratio of $\frac{m}{M}$ is

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

Answer 1

Answer: (C)

$\frac{16}{9}$

Answer 2

$T=2\pi \sqrt{\frac{M}{k}}$ $T=2\pi \sqrt{\frac{M+m}{k}}$ $\Rightarrow$ $\frac{5T}{3}=2\pi \sqrt{\frac{M+m}{k}}$ Dividing E (i) by Eq (ii), we have $\frac{3}{5}=\sqrt{\frac{M}{M+m}}$ $\frac{9}{25}=\frac{M}{M+m}$ $\Rightarrow$ $9M+9m=25M$ $\Rightarrow$ $16M=9m$ $\frac{m}{M}=\frac{16}{9}$