Q. A mass $m$ attached to a spring oscillates every $2\ s.$ If the mass is increased by $2\ kg,$ then time-period increases by $1\ s.$ The initial mass is
A) $1.6\ kg$
B) $3.9\ kg$
C) $9.6\ kg$
D) $12.6\ kg$
Explanation
(a) $T = 2\pi\sqrt{\frac{m}{k}} \Rightarrow \frac{T_{2}}{T_{1}} = \sqrt{\frac{m_{2}}{m_{1}}} \Rightarrow \frac{3}{2} = \sqrt{\frac{m + 2}{m}} \Rightarrow \frac{9}{4} = \frac{m + 2}{m}$
$\Rightarrow m = \frac{8}{5}kg = 1.6\ kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.