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Two particles, 1 and 2, each of mass π, 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 and angular frequency π. Thus, their positions at time π‘ are given by \(x_1 (t) = (x_0 + d) + \alpha \ sin \omega t\) and \(x_2t = (x_0 -d) β \alpha sin \ wt,\) respectively, where \(π > 2π.\) Particle 3 of mass π moves towards this system with speed π’0 = ππ/2, and undergoes instantaneous elastic collision with particle 2, at time \(π‘_0\). Finally, particles 1 and 2 acquire a center of mass speed \(π£_{cm}\) and oscillate with amplitude π and the same angular frequency π.
Question: 1
If the collision occurs at time \(π‘_0 = 0\), the value of \(\frac{π£_cm}{(\alpha\omega)}\) will be __________
If the collision occurs at time \(π‘_0 = 0\), the value of \(\frac{π£_cm}{(\alpha\omega)}\) 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 \(π‘_0 =\frac{\pi}{(2\omega)}\), then the value of \(4π^2/π^2\) will be ________
If the collision occurs at time \(π‘_0 =\frac{\pi}{(2\omega)}\), then the value of \(4π^2/π^2\) will be ________
Updated On: Jun 20, 2024
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Correct Answer: 4.25
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The correct answer is :4.25
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