Q. If a body of mass m is moving on a rough horizontal surface of coefficient of kinetic friction μ, the net electromagnetic force exerted by surface on the body is –

(A)mg(1 + μ^2)^1/2

(B)μmg

(C)mg

(D)mg(1 – u^2)^1/2

To tackle this question, we need to analyze the forces acting on a body of mass \( m \) moving on a rough horizontal surface with a coefficient of kinetic friction \( \mu \). The question asks for the net electromagnetic force exerted by the surface on the body. However, it's important to clarify that the primary forces at play here are gravitational force and frictional force, rather than electromagnetic forces.

Understanding the Forces Involved

When a body is on a horizontal surface, the gravitational force acting on it is given by:

• Weight (W): \( W = mg \)

Here, \( g \) is the acceleration due to gravity. This weight acts downward, and the surface exerts an equal and opposite force known as the normal force \( N \), which acts upward. For a horizontal surface with no vertical acceleration, the normal force is equal to the weight of the body:

• Normal Force (N): \( N = mg \)

Frictional Force

Next, we consider the frictional force, which opposes the motion of the body. The kinetic frictional force \( f_k \) can be calculated using the coefficient of kinetic friction \( \mu \):

• Kinetic Friction (f_k): \( f_k = \mu N = \mu mg \)

Net Force Analysis

In this scenario, the net force acting on the body in the horizontal direction is the frictional force, which opposes the motion. However, the question specifically asks for the net electromagnetic force, which is somewhat misleading since we are primarily dealing with mechanical forces here. The electromagnetic forces are not directly relevant unless specified otherwise.

Since the body is moving, the net force in the horizontal direction can be expressed as:

• Net Force (F_net): \( F_{\text{net}} = -f_k = -\mu mg \)

Choosing the Correct Option

Given the options provided in the question, we can see that the only relevant force that corresponds to our analysis is:

• (B) \( \mu mg \)

This option represents the magnitude of the kinetic frictional force acting on the body, which is the primary force opposing its motion on the rough surface. Therefore, the correct answer to the question is:

Answer: (B) \( \mu mg \)

Conclusion

In summary, while the question mentions electromagnetic forces, the context of the problem is more about the mechanical forces at play due to gravity and friction. The kinetic friction force is what we calculated, and it directly relates to the coefficient of kinetic friction and the weight of the body. Understanding these forces helps clarify the dynamics of motion on rough surfaces.