A basketball hits the Earth and bounces off it with the same speed in an elastic

Question

A basketball hits the Earth and bounces off it with the same speed in an elastic collision. With reference to a system containing the Earth and the ball, which of the following statements applies?

a. The momentum of the basketball is conserved because it bounces with the same speed.

b. Momentum is not conserved in this particular type of collision.

c.The momentum change of the ball is equal and opposite to the momentum change of the earth.

d. Momentum conservation law is violated any time when gravity is involved.

I'm stuck between a and c. Please help!!

Explanation / Answer

If we take the momentum as a positive in the direction of positive y axis then in the above case the change in momentum will be as follows

Momentum initial = - m*v

I take negative sign because the direction of ball is downward.

Momentum final = m*v

So change in momentum = final momentum - initial momentum

= 2mv

So option A is wrong as the momentum is not conserved. Because change in momentum is not zero.

Option c is also not correct because momentum change of ball is 2mv and the momentum change of earth is zero as there is not any change in velocity of earth due to collision.

Option b is incorrect because momentum is conserved along x axis as no force acting along x axis. and here they do not mentioned any axis.

So option d is right.

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