Comprehension

Two particles, 1 and 2, each of mass π‘š, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at \(π‘₯_0\), are oscillating with amplitude π‘Ž and angular frequency πœ”. Thus, their positions at time 𝑑 are given by \(x_1 (t) = (x_0 + d) + \alpha \  sin \omega t\) and \(x_2t = (x_0 -d) βˆ’ \alpha sin \ wt,\) respectively, where \(𝑑 > 2π‘Ž.\) Particle 3 of mass π‘š moves towards this system with speed 𝑒0 = π‘Žπœ”/2, and undergoes instantaneous elastic collision with particle 2, at time \(𝑑_0\). Finally, particles 1 and 2 acquire a center of mass speed \(𝑣_{cm}\) and oscillate with amplitude 𝑏 and the same angular frequency πœ”.
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Question: 1

If the collision occurs at time \(𝑑_0 = 0\), the value of \(\frac{𝑣_cm}{(\alpha\omega)}\) will be __________

Updated On: Jun 20, 2024
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Correct Answer: 0.75

Solution and Explanation

The correct answer is :00.75
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Question: 2

If the collision occurs at time \(𝑑_0 =\frac{\pi}{(2\omega)}\), then the value of \(4𝑏^2/π‘Ž^2\) will be ________

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Correct Answer: 4.25

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The correct answer is :4.25
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