The correct options are (c) and (d). The magnetic force acts perpendicular to the direction of motion of the proton. It does not change its mass and speed but changes its direction of motion. So both velocity and momentum get changed.

When the proton is moving with velocity "v" in a region where magnetic field "B" exists the force acting on the proton is given by,
F = q(v x B) where q = charge on proton
Due to this force the proton accuires another velocity in a direction perpendicular (since it is cross product) to that of the initial velocity. So, both net velocity and net momentum will change. But the momentum in the direction in which proton is moving may not change since force is not acting in this direction.

Explanation:

When a proton moves freely in a magnetic field, it experiences a force called the magnetic force. This force acts perpendicular to both the velocity of the proton and the magnetic field. As a result, the proton undergoes a change in its motion. Let's examine each property and determine if it can change while the proton moves in a magnetic field.

Mass:
The mass of a proton is an intrinsic property that does not change. It remains constant regardless of its motion or the presence of a magnetic field. Therefore, the mass of a proton does not change while it moves in a magnetic field.

Speed:
The speed of a proton is the magnitude of its velocity vector. When a proton moves in a magnetic field, its speed can remain constant if there is no external force acting on it. However, if there are other forces present, such as a gravitational force or an electric force, the speed of the proton may change. Therefore, the speed of a proton can change while it moves in a magnetic field, but this change is not directly caused by the magnetic field itself.

Velocity:
Velocity is a vector quantity that includes both the speed and direction of an object. When a proton moves in a magnetic field, its velocity can change. The magnetic force acts perpendicular to the velocity vector, causing the proton to change its direction. Therefore, the velocity of a proton can change while it moves in a magnetic field.

Momentum:
Momentum is the product of an object's mass and velocity. Since the mass of a proton does not change and its velocity can change in a magnetic field, the momentum of a proton can also change. The direction of the momentum vector will change due to the change in velocity caused by the magnetic force.

Conclusion:
In summary, while a proton moves freely in a magnetic field, its mass remains constant, but its speed, velocity, and momentum can change. The magnetic force acting on the proton causes a change in its motion, leading to changes in speed, velocity, and momentum.