Question

A small particle travelling with a velocity v collides elastically with a spherical body of equal mass radius r initially kept at rest.The centre of this spherical body is located a distance away from the direction of motion of the particle (given figure).Find the final velocities of the two particles.

Answer 1

Let the mass of the both the particle and the spherical body be 'm',the particle velocity 'v' has two components $vcos\alpha$ normal to the sphere and $vsin\alpha$ tangential to the sphere.

After the collision,they will exchange their velocities.So,the spherical body will have a velocity $vcos\alpha$ and the particle will not have any component of velocity in this direction.

[The collision will be due to the component $vcos\alpha$ in the normal direction.

But,the tangential velocity,of the particle $vsin\alpha$ will be unaffected.]

So,velocity of the sphere=$vcos\alpha$

$=\frac{v}{r}\sqrt{r^2-{\rho }^2}$

and velocity of the particle=$vsin\alpha$

$=\frac{\rho v}{r}$