Question

A body of mass $m$ collision obliquely with another identical body at rest. Assuming collision to be elastic. The colliding body will move at an angle of:
A. ${60^ \circ }$ to one another
B. ${90^ \circ }$ to one another
C. ${120^ \circ }$ to one another
D. ${30^ \circ }$ to one another

Answer 1

Hint: In an oblique collision the body at rest will gain some momentum such as the momentum of the system remains conserved and the kinetic energy also remains conserved. In an oblique elastic collision, the momentum is conserved in both X as well as Y directions separately.

Complete step by step answer:
When a moving body interacts with another body at rest or in motion, the momentum and the energy of the system must remain conserved unless there is some energy loss or an unbalanced external force is applied to the system. A collision in which there is no loss of energy in any form is known as elastic collision.
When identical body masses collide, their velocities are interchanged. As a result, the body at rest will start moving with the velocity at which the first ball was moving. For an elastic collision with bodies having equal mass, the bodies after collision move perpendicular to each other so, as the momentum of the system remains conserved.
As bodies move perpendicularly at an angle of ${90^ \circ }$ with respect to each other, option B is the correct option.

So, the correct answer is “Option B”.

Note:
If the bodies move in some other angle the momentum won’t be conserved in X and Y directions. As the second body was initially at rest, it will start moving at some angle and the first body will move in an angle complementary to the second body. We can also prove this by conserving the momentum in X and Y directions. Do not confuse between oblique and elastic collisions.