Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision
A small particle travelling with a velocity v undergoes an elastic collision with a spherical body of equal mass and radius r initially kept at rest. As shown in the figure, the centre of the spherical body is situated a distance ,(
Options
- ASmall particle moves along the initial direction with speed v r ; spherical body moves perpendicular to the in
- BSmall particle moves along the tangent with speed v 2r ; spherical body moves perpendicular to the small parti
- CSmall particle moves along the normal with speed v r r^2 - ^2 ; spherical body moves perpendicular to the smal
- DSmall particle moves along the tangent with speed v r ; spherical body moves perpendicular to the small partic
Correct answer
D. Small particle moves along the tangent with speed v r ; spherical body moves perpendicular to the small partic
Step-by-step solution
Let the angle between the initial velocity of the small particle and the line of impact (normal to the sphere at the point of contact) be . From the geometry of the collision, = r and = r^2 - ^2 r . The initial velocity of the small particle can be resolved into two components: Normal component: v_n = v Tangential component: v_t = v The spherical body is initially at rest. Since the collision is elastic and the masses of the two bodies are equal, they exchange their velocities along the line of impact (normal direc