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JEE Main 2021 (25 Jul, Shift 1) · Spring Systems

Spring Systems question from JEE Main 2021 (25 Jul, Shift 1)

Q76JEE Main 2021 · 25 JUL · SHIFT 1Difficult

Spring Systems

In the reported figure, two bodies A and B of masses 200 g and 800 g 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 ____________ rad/s when k = 20 N/m.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 10

  1. Springs kk and 4k4k in series: keq=k⋅4k5k=4k5=16 N/mk_{eq} = \frac{k \cdot 4k}{5k} = \frac{4k}{5} = 16\text{ N/m}.
  2. Reduced mass μ=0.2×0.81.0=0.16 kg\mu = \frac{0.2 \times 0.8}{1.0} = 0.16\text{ kg}.
  3. ω=keqμ=160.16=10 rad/s\omega = \sqrt{\frac{k_{eq}}{\mu}} = \sqrt{\frac{16}{0.16}} = 10\text{ rad/s}
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