The frequency of oscillation of a mass ……

Single correct+4 / -1Answer matches NTA’s final key

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$ . If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$ . The value of $v_2/v_1$ is ______.

1
2
$\sqrt2$
$\sqrt3$

Solution

A spring's constant is inversely proportional to its length ( $kl$ is constant), so half the spring has constant $2k$ .

$v = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \;\Rightarrow\; \frac{v_2}{v_1} = \sqrt{\frac{2k}{k}} = \sqrt2.$

Answer: $\sqrt2$ .

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Oscillations and Waves

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