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MHT CET 2025 (21 Apr, Shift 1) · Spring Systems

Spring Systems question from MHT CET 2025 (21 Apr, Shift 1)

Q27MHT CET 2025 · 21 APR · SHIFT 1Medium

Spring Systems

A mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period $T$ . If the mass is increased by $m_0$ , the periodic time becomes $\frac{5T}{4}$ . The ratio $\frac{m_0}{M}$

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Answer: (c)

$T \propto \sqrt{m}$ : $\left(\frac{5}{4}\right)^2 = \frac{m + m_0}{m}$ .
$\frac{25}{16} = 1 + \frac{m_0}{m} \Rightarrow \frac{m_0}{m} = \frac{9}{16}$
( $M$ in the question is the original mass $m$ .) So the answer is (c) $\frac{9}{16}$ .

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