Understanding the conditions under which a body will move requires considering the forces acting upon it, particularly the applied force and the force of friction. Friction is a resistive force that opposes the relative motion or tendency of motion between two surfaces in contact. For a body to initiate movement from rest, the applied force must be sufficient to overcome this opposing frictional force.

Friction and Body Movement

When an external applied force tries to move a body, a frictional force develops at the contact surface, opposing the motion. There are two main types of friction relevant here:

• Static Friction ($F_s$): This force acts when the body is at rest and there is a tendency for motion. Static friction can vary from zero up to a maximum value ($F_s^{\text{max}}$). The body remains at rest as long as the applied force is less than or equal to this maximum static friction.
• Kinetic Friction ($F_k$): This force acts when the body is already in motion. Kinetic friction is generally constant for a given pair of surfaces and is usually less than the maximum static friction ($F_k < F_s^{\text{max}}$).

For a body will move from rest, the applied force must exceed the maximum static friction. Once the body is in motion, its movement (acceleration or constant velocity) depends on the relationship between the applied force and the kinetic friction.

Condition for Body to Move

The crucial condition for a body to move from a state of rest, or to accelerate if already moving, is that the applied force must be greater than the opposing force of friction. This ensures a net force acts on the body in the direction of the applied force, causing it to accelerate.

Analyzing Options for Body Motion

Let's evaluate each given option to determine the correct condition for when the body will move:

• Option 1: Force of friction = applied force

  If the force of friction is equal to the applied force ($F_{\text{friction}} = F_{\text{applied}}$), the net force on the body is zero. If the body is initially at rest, it will remain at rest (up to the point where applied force equals maximum static friction). If the body is already moving, it will continue to move at a constant velocity (when applied force equals kinetic friction). This condition does not guarantee that the body will move or start moving from rest; it primarily describes equilibrium or constant velocity.

• Option 2: Force of friction < applied force

  This is the correct condition for a body to move or accelerate. When the applied force is greater than the opposing force of friction ($F_{\text{applied}} > F_{\text{friction}}$), there is a net force acting on the body in the direction of the applied force. If the body is at rest, and $F_{\text{applied}} > F_s^{\text{max}}$, the body will begin to move. If the body is already moving, and $F_{\text{applied}} > F_k$, the body will accelerate. This positive net force ensures the body will move or increase its speed.

  Mathematically, this condition can be represented as: $F_{\text{friction}} < F_{\text{applied}}$

• Option 3: Force of friction > applied force

  If the force of friction is greater than the applied force ($F_{\text{friction}} > F_{\text{applied}}$), the net force on the body opposes the direction of intended motion. If the body is at rest, it will not move. If the body is already moving, it will decelerate and eventually come to a stop. Therefore, this condition does not result in the body moving or continuing its motion in the desired direction.

• Option 4: All of the above

  Based on the detailed analysis of each option, only one condition correctly describes when a body will move by initiating motion or accelerating.

Therefore, for a body to move, the applied force must overcome the resistive force of friction, meaning the force of friction must be less than the applied force.