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MHT CET 2024 (2 May, Shift 2) · Spring Systems

Spring Systems question from MHT CET 2024 (2 May, Shift 2)

Q37MHT CET 2024 · 2 MAY · SHIFT 2Easy

Spring Systems

A spring has a certain mass suspended from it and its period of vertical oscillations is $T_1$ . The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$ . The ratio of $T_2/T_1$ is

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Answer: (b)

$k \propto \frac{1}{\text{length}}$ , so each half has $k' = 2k$ .
$T = 2\pi\sqrt{m/k} \Rightarrow \frac{T_2}{T_1} = \sqrt{\frac{k}{2k}} = \frac{1}{\sqrt{2}}$ .
So the answer is (b) $1:\sqrt{2}$ .

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