Question

A ball of mass m collides with the ground with velocity v and rebounds with the same speed. The change in momentum will be:
1. mv
2. -2mv
3. -mv
4. zero

Answer 1

Correct Answer - Option 2 : -2mv

CONCEPT:

• Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.

P = mv

where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

• Momentum is the vector quantity.

EXPLANATION:

Momentum P = mv

Since momentum is a vector quantity.

Initially, the ball is moving in a downward direction.

\(P_{initial} = mv (- ̂{j})\)

\(P_{initial} = -mv~ ̂{j}\)

After the collision with the ground, it moves in the upper direction with the same speed. so

\(P_{final} = mv~ ̂{j}\)

Change in Momentum = P_final - P_initial 

Change in Momentum = \( -mv~ \hat{j}- mv~ \hat{j}= -2mv~ \hat{j}\)

So change in momentum is -2mv.

Hence the correct answer is option 2.