Question

which of the following provides a correct prediction about the change in the momentum of the two - block system with correct justification?
a the change in momentum of the system is negative because kinetic energy is lost in the collision.

b the change in momentum of the system is negative because the blocks have a speed less than $v_0$ after the collision.

c the change in momentum of the system is zero because there is no net external force exerted on the system.

d the change in momentum of the system is zero because the kinetic energy of the system is constant during the collision

Explanation:

To determine the correct option, we analyze the principle of conservation of momentum. The law of conservation of momentum states that the total momentum of a system remains constant (change in momentum is zero) if there is no net external force acting on the system.

• Option A: Kinetic energy loss (like in an inelastic collision) doesn't affect momentum conservation. Momentum depends on mass and velocity, not kinetic energy directly. So this is incorrect.
• Option B: The speed after collision being less than \( v_0 \) doesn't determine the change in momentum. Momentum change depends on net external force, not just speed. This is incorrect.
• Option C: For a two - block system during a collision, the internal forces (like the forces between the two blocks during collision) are action - reaction pairs and cancel out. So there is no net external force on the system. By the law of conservation of momentum, the change in momentum of the system (\(\Delta p\)) is zero because \(\Delta p = F_{net,external}\times\Delta t\) and \(F_{net,external} = 0\). This is correct.
• Option D: In a collision (especially if it's inelastic), kinetic energy is not constant (it can be lost). But momentum is conserved due to no net external force, not because kinetic energy is constant. So this is incorrect.

Answer:

C. The change in momentum of the system is zero because there is no net external force exerted on the system.