Question

Two spheres A and B, of equal radii, lie at rest on a smooth horizontal table. Sphere A has mass 2m kg and sphere B has mass 16m kg. Sphere A is projected with speed 3 ms

Answer 1

Before collision

`rarrV_A = 3m/s`

`rarr V_B = 0m/s`

After collision

`rarr V_A = V1`

`rarr V_B = V2`

Using the momentum conservation;

`rarr2mxx3 = 2mV1+16mV2`

`3 = V1+8V2 ----(1)`

Using the definition of coefficient of restitution;

`rarr 0.5(3-0) = V1-V2`

`1.5 = V1-V2 ----(2)`

(1)-(2)

`1.5 = 9V2`

`V2 = 1/6`

From (1);

`V1 = 8/3`

So both spheres travels in the initial direction of A after collision. The velocity of A is ` ` and velocity of B is ` ` .

Note

It is assumed that the direction of spheres before and after the collision remains in the same line.