The total momentum of the ball and the earth is conserved
The total mechanical energy of the ball and the earth is conserved
Hide Solution
Verified By Collegedunia
The Correct Option isC
Solution and Explanation
When a ball hits the floor and rebounds, it interacts with the Earth. During an inelastic collision, kinetic energy is not conserved. However, momentum is always conserved in a closed system. In this case, the closed system comprises both the ball and the Earth.
(A) the momentum of the ball is conserved: Incorrect. The ball's momentum changes direction after rebounding.
(B) the mechanical energy of the ball is conserved: Incorrect. In an inelastic collision, some kinetic energy is transformed into other forms of energy, such as heat and sound. Therefore, the ball's mechanical energy is not conserved.
(C) the total momentum of the ball and the earth is conserved: Correct. The Earth's large mass means its velocity change is negligible, but the momentum transfer is significant enough to change the ball's momentum. The total momentum of the system remains constant.
(D) the total mechanical energy of the ball and the earth is conserved: Incorrect. While the total energy is conserved, mechanical energy is specifically not conserved in an inelastic collision. Some of the initial mechanical energy is converted to other forms of energy.
The correct answer is (C) the total momentum of the ball and the earth is conserved.
