The diagram shows two identical spheres X and Y. Initially, X moves with speed v directly towards Y.

Q#175: [Dynamics > Collisions] (Past Exam Paper – November 2006 Paper 1 Q11 & June 2010 Paper 11 Q12 & June 2010 Paper 12 Q10)

The diagram shows two identical spheres X and Y.


Initially, X moves with speed v directly towards Y. Y is stationary. The spheres collide elastically.
What happens?




Solution 175:
Answer: D.
For elastic collision, both the momentum and kinetic energy are conserved.

Let mass of 1 sphere = m

Before collision,
Momentum = mv

Kinetic energy = ½ mv2

After collision,
Momentum should be conserved.

For A, momentum is conserved.

B is an impossible case since it would imply that sphere Y does not exist (even though momentum is conserved, this is physically impossible).

For C, sum of (magnitude of) momentum after collision is mv (but the spheres moves in opposite directions).

For D, momentum is conserved

If the speeds of both spheres become ½ v [as suggested by A and C],

Sum of Kinetic energies after collision = ½ m(v/2)2 + ½ m(v/2)2 = mv2/4

Kinetic energy is not conserved in these 2 cases (A and C).

Only choice D will have both the momentum and kinetic energy conserved.

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