Question

The sphere of mass m moving with velocity u is involved in an elastic collision with a sphere of mass 2m moving along the same line with velocity U. Find the velocity of the sphere after Impact.

a) 1/3U
b) 1/2U
c) U
d) 2/3U

Answer 1

To find the velocity of the sphere after impact, we need to apply the conservation of momentum and kinetic energy principles. We can set up equations using these principles and solve for the velocities of the spheres after the impact.

Step-by-step explanation:

In an elastic collision, both the momentum of the system and its kinetic energy are conserved. To find the velocity of the sphere after the impact, we can solve it using these conservation principles.

Let v₁ and V₁ be the velocities of the spheres of mass m and 2m respectively after the impact. According to the rules of the Conservation of momentum, the initial momentum of the system is similar to the final momentum of the system:

1. Initial momentum = m * u + 2m * U
2. Final momentum = m * v₁ + 2m * V₁
3. m * u + 2m * U = m * v₁ + 2m * V₁

Similarly, according to the conservation of kinetic energy, the initial kinetic energy of the system is equal to the final kinetic energy of the system:

1. Initial kinetic energy = 1/2 * m * u² + 1/2 * 2m * U²
2. Final kinetic energy = 1/2 * m * v₁² + 1/2 * 2m * V₁²
3. 1/2 * m * u² + m * U² = 1/2 * m * v₁² + 2m * V₁²

Solving these two equations simultaneously will give us the values of v₁ and V₁ after the impact.