Q. 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 simple harmonic oscillations with a time period $T.$ If the mass is increased by $m$ then the time period becomes $\left( \frac{5}{4}T \right).$ The ratio of $\frac{m}{M}$ is
A) 9/16
B) 25/16
C) 4/5
D) 5/4
Explanation
(a) $T = 2\pi\sqrt{\frac{m}{K}} \Rightarrow m \propto T^{2} \Rightarrow \frac{m_{2}}{m_{1}} = \frac{T_{2}^{2}}{T_{1}^{2}}$
$\Rightarrow \frac{M + m}{M} = \left( \frac{\frac{5}{4}T}{T} \right)^{2} \Rightarrow \frac{m}{M} = \frac{9}{16}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.