Question

A body of 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 $1kg$, the time period of oscillations becomes $5s$. The value of $m$ in $kg$ is

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

Answer 1

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

For spring mass system time period is given by,
$T=2\pi \sqrt{\frac{m}{k}}3=2\pi \sqrt{\frac{m}{k}}--\left(1\right)\mathrm{The}\mathrm{time}\mathrm{period}\mathrm{of}\mathrm{system}\mathrm{when}\mathrm{mass}\mathrm{increased}\mathrm{by}1kg5=2\pi \sqrt{\frac{m+1}{k}}--\left(2\right)\mathrm{squaring}\mathrm{and}\mathrm{then}\mathrm{dividing}\mathrm{equation}(1)\mathrm{by}(2)\frac{9}{25}=\frac{m}{m+1}\Rightarrow m=\frac{9}{16}$