Q73 / 90 · JEE Main 2024 (01 Feb Shift 2) · Physics

A mass $m$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_{1} .$ The frequency of oscillations if a mass $9 m$ is suspended from the same spring is $f_{2} .$ The value of $\frac{f_{1}}{f_{2}}$ is _____ .

Correct answer: 3

Solution

Frequency of oscillation of a spring-block system is given by, $f = \frac{1}{2 π} \sqrt{\frac{k}{m}}$

Therefore, for both cases, we can write

$f_{1} = \frac{1}{2 π} \sqrt{\frac{k}{m}}$ and

$f_{2} = \frac{1}{2 π} \sqrt{\frac{k}{9 m}}$

Required ratio, $\frac{f_{1}}{f_{2}} = \sqrt{\frac{9}{1}} = \frac{3}{1}$

Hence, the correct answer is 3.