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JEE Main 2022 (24 Jun, Shift 2) · Spring Systems

Spring Systems question from JEE Main 2022 (24 Jun, Shift 2)

Q57JEE Main 2022 · 24 JUN · SHIFT 2Medium

Spring Systems

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:

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Answer: (b)

  1. vmax=Aωv_{max} = A\omega, so equal vmaxv_{max} gives A1A2=ω2ω1\frac{A_1}{A_2} = \frac{\omega_2}{\omega_1}.
  2. ω12=2k0.05=40k\omega_1^2 = \frac{2k}{0.05} = 40k, ω22=9k0.1=90k\omega_2^2 = \frac{9k}{0.1} = 90k
  3. A1A2=9040=32\frac{A_1}{A_2} = \sqrt{\frac{90}{40}} = \frac{3}{2}
  4. So the answer is (b) 3 : 2.
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