A body whose momentum is constant must have constant velocity.

For a given mass, the velocity remains constant if the momentum is constant.

This is because momentum = mass × velocity.

So, momentum is directly proportional to velocity.

Hence option B) is correct

Momentum and its relation to force and velocity

Momentum:
Momentum is a fundamental concept in physics that describes the motion of an object. It is defined as the product of an object's mass and its velocity. The formula for momentum is:

Momentum (p) = mass (m) * velocity (v)

Constant Momentum:
When the momentum of a body is constant, it means that the product of its mass and velocity remains the same over time. In other words, the body's mass and velocity may change, but their product remains constant.

Relation to Force:
Force is defined as the rate of change of momentum. It is the external influence that can cause a change in an object's momentum. According to Newton's second law of motion, force is directly proportional to the rate of change of momentum. Mathematically, it can be expressed as:

Force (F) = rate of change of momentum = Δp/Δt

Since the momentum of the body in question is constant, the rate of change of momentum is zero. Therefore, the force acting on the body must be zero as well. In other words, a body with constant momentum experiences no net force acting on it.

Relation to Velocity:
The velocity of a body is defined as the rate of change of its position with respect to time. When the momentum of a body is constant, it implies that the product of its mass and velocity remains constant. Therefore, if the mass of the body is constant, its velocity must also remain constant.

Conclusion:
In conclusion, a body with constant momentum must have a constant velocity. This is because the product of mass and velocity, which defines momentum, remains constant. The body experiences no net force, as the rate of change of momentum is zero. However, it is important to note that the body's mass can change, which would then require a corresponding change in velocity to maintain constant momentum.