To answer the question about the requirements for maintaining constant velocity of a particle on a frictionless surface, let's analyze the situation using Newton's laws of motion.

Concept: According to Newton's First Law of Motion (also known as the law of inertia), an object will remain at rest or move at a consistent velocity unless acted upon by a net external force.

When a particle is moving on a frictionless surface, there is no friction force acting on it to change its motion. In such scenarios:

• If the particle is already moving with constant velocity, it has zero acceleration because there is no resultant force.
• No additional external force is necessary to keep the particle moving, since there is no opposing force (friction) to overcome.

Analysis of Options:

• Should act continuously: This option suggests the need for a constant force to maintain velocity, which is incorrect due to the absence of any opposing forces on a frictionless surface.
• Should act opposite to the direction of motion: This would decelerate the particle, contrary to maintaining constant velocity.
• Is not necessary (Correct Answer): As explained, no force is needed to keep a particle moving at constant velocity on a frictionless surface.
• Should be of variable magnitude: This implies continuously changing the force, which again is unnecessary when no net external force is required.

Therefore, to keep a particle moving with constant velocity on a frictionless surface, an external force is not necessary.