Question

A body mass $m$ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released, it oscillates with a time period of $3s$. When the mass $m$ is increased by $2kg$, the time period of oscillations becomes $5s$. The value of $m$ in $kg$ is

• A. $\frac{9}{8}$
• B. $\frac{4}{3}$
• C. $\frac{16}{9}$
• D. $\frac{9}{16}$

Answer 1

The correct option is A $\frac{9}{8}$

Time period of simple spring-mass system is,
$T_1=2\pi \sqrt{\frac{m}{k}}=3s-----\left(1\right)$
When mass incresed by $2kg$, time period becomes
$T_2=2\pi \sqrt{\frac{m+2}{k}}=5s----\left(2\right)$
Dividing equation (2) by equation (1),
$\frac{T_2}{T_1}=\sqrt{\frac{m+2}{m}}=\frac{5}{3}$
$\frac{m+2}{m}=\frac{25}{9}$
$1+\frac{2}{m}=\frac{25}{9}$
$\frac{2}{m}=\frac{16}{9}$
$m=\frac{9}{8}kg$