Question

All external forces on the body cancel out. Which statement must be correct?

A The body doesn't move.
B the momentum of the body remains unchanged.
C The speed of the body remains unchanged.
D The total energy ( kinetic and potential ) pf the body remains unchanged.

Give reasons for your answer.

Answer 1

`B.`The momentum of the body remains unchanged.

Explanation:

As there is no external force acting on the body, the momentum remains conserved (in whichever direction the external force is absent).

Answer 2

Obviously not A... `darrdarr`

Explanation:

A is incorrect. If all external forces on the body cancel out, the body may be moving with a constant velocity with `a=0`. So, it depends on the body's initial state of motion.

B is correct. Here, the law of conservation of momentum is applied.

C is correct. If the momentum of the body remains unchanged, the speed also doesn't change.

D is correct. The total Mechanical energy ( kinetic + potential ) of the body will remain unchanged.

`-------------`

EDIT: (After the comment by @UmAir Ansar)

C is correct, if nothing else changes (mentioned above) . But if the mass of the body is changing , (like a rocket ejecting some of its fuel) the speed of the body will change. So, C can be considered `color(red)("incorrect"`.

D can be considered `color(red)("incorrect"` as it is mentioned "Total Energy" here. Total energy is not comprised only of kinetic and potential energies.

So, we can conclude that B is the only consistent statement here, which does not contradict anything else. So B is the `color(green)("correct"` answer. (because we want only 1 `color(green)("correct"` answer.)