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A particle of mass m moving along the x-axis with velocity u collides elastically with a stationary particle of mass 10m. After the collision the first particle carries away half of its original kinetic energy and is deflected by angle theta1 from the x-axis, while the second particle moves at angle theta2. If sin(theta1) = sqrt(n) * sin(theta2), find the integer value of n.

1. 2
2. 5
3. 6
4. 10

Correct answer: 6

Solution

Conserving momentum components and using KE1 = KE0/2 with elastic energy conservation yields sin(theta1) = sqrt(6) sin(theta2), so n = 6 (JEE Advanced 2020).

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