Question

Q) Two spheres of equal mass, one at rest collide with the collision being absolutely elastic but not central. Then the angle between the velocities must be a) 180° b)90°

Answer 1

Two spheres of equal mass, one at rest collide with the collision being absolutely elastic but not central. Then the angle between the velocities must be 90 degrees. (oblique collision) for proof, have a look at the attached files

Answer 2

Answer:

If the two spheres are of equal masses, one at rest and other in motion and the collision being elastic then we can use the energy conservation formulae.

where initial velocity is u1 and final velocity v1 and v2. Let the collision between the two have angle (Ф and θ).

Thus we get the value of u1^2 = v1^2 + v2^2 + v1v2cos(Ф + θ).

Again, according to law of conservation of  linear momentum we get.

u1^2 = v1^2 + v2^2.

Then putting the value of u1 we get.

cos(Ф + θ)=0

Ф + θ = 90.