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 $3\,s$. When the mass $m$ is increased by $1\,kg$, the time period of oscillations becomes $5\, s$. The value of $m$ in $kg$ is

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

Answer 1

Answer: (D)

$3 = 2\pi \sqrt{\frac{m}{k}} $
$ 5=2\pi\sqrt{\frac{m+1}{k}} $
$ \frac{3}{5} = \sqrt{\frac{m}{m+1}} $
$ \frac{9}{25} = \frac{m}{m+1} $
$ 9m+9=25m $
$ 16m = 9 $
$ m = \frac{9}{16} $