Two identical elastic spheres, each of mass m, are at rest on a smooth table and touch each other. They are struck symmetrically by an identical elastic sphere, but of mass M, having a velocity u, perpendicular to the line of centres of the two stationary spheres. The mass M comes to rest immediately after the collision. If m = 2kg, what is M in kg.

Engineering

Physics

Center of Mass

Collision

Momentum and Energy Conservation for System of Particles

Question

Two identical elastic spheres, each of mass m, are at rest on a smooth table and touch each other. They are struck symmetrically by an identical elastic sphere, but of mass M, having a velocity u, perpendicular to the line of centres of the two stationary spheres. The mass M comes to rest immediately after the collision. If m = 2kg, what is M in kg.

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Mu = 2mv cos 30°

$1 = e = \frac{v - 0}{ucos 30^{\circ} - 0}$

$v = \frac{Mu}{m \sqrt{3}}$

$1 = \frac{\frac{Mu}{m \sqrt{3}}}{u \times \frac{\sqrt{3}}{2}}$

$\frac{M}{m} = \frac{3}{2} \Rightarrow M = 3 kg$