In the reported figure, two bodies A andB… - JEE Main 2021 Physics PYQ

JEE Main 2021 — Physics Waves & Oscillations

2021integermedium

In the reported figure, two bodies $A\mathrm{and}B$ of masses $200g$ and $800g$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ $\mathrm{rad}{s}^{-1}$ when $k=20N{m}^{-{1}^{}}$ .

JEE Main 2021 Physics, Oscillations — question figure

Official previous-year question

Held on 25 Jul 2021 · Verified 6 Jul 2026.

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Solution

$\omega =\sqrt{\frac{{k}_{\mathrm{eq}}}{\mu }}$

$\mu =$ reduced mass

Springs are in series connection,

${k}_{\mathrm{eq}}=\frac{{k}_{1}{k}_{2}}{{k}_{1}+{k}_{2}}$

${k}_{\mathrm{eq}}=\frac{k\times 4k}{5k}=\frac{4k}{5}$

${k}_{\mathrm{eq}}=\frac{4\times 20}{5}N{m}^{-1}=16N{m}^{-1}$

$\mu =\frac{{m}_{1}{m}_{2}}{{m}_{1}+{m}_{2}}=\frac{0.2\times 0.8}{0.2+0.8}=0.16\mathrm{kg}$

$\omega =\sqrt{\frac{16}{0.16}}=\sqrt{100}=10$

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