Question

A small particle traveling with a velocity v collides elastically with a spherical body of equal mass and of radius r initially kept at rest. The center of this spherical body is located a distance ρ( < r ) away from the direction of motion of the particle (figure 9-E23). Find the final velocities of the two particles.

[Hint : The force acts along the normal to the sphere through the contact . Treat the collision as one-dimensional for this direction . In the tangential direction no force acts and the velocities do not change].

Answer 1

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ANSWER::

Let mass of both particle and spherical body be m.

Now see figure

Particle velocity ( v ) has two components :-

v cos α is normal to the sphere

v sin α is tangential to the sphere

After collision , velocities gets exchanged .

So , the spherical body will have a velocity v cos α and particle will not have any component of velocity in this direction.

Collision happened because the component v cos α is in normal direction

But , the tangential velocity of particle v sin α will be unaffected.

Now , velocity of sphere = v cos α = v√(r² - ρ²) / r

Velocity of particle = v sin α = vρ / r

Hope it helps!