Problem Statement:
A heavy rope of mass 10 kg and length 8 m is lying on a horizontal smooth surface. A horizontal force of 40 N is applied at one end. Calculate the tension at the midpoint.

Solution:
To solve the problem, we need to consider the forces acting on the rope. There are three forces acting on the rope:

1. Force applied at one end of the rope
2. Weight of the rope
3. Tension force at the midpoint of the rope

Let's analyze each force in detail.

1. Force applied at one end of the rope:
The force applied at one end of the rope is 40 N. This force will cause the rope to move in the direction of the force.

2. Weight of the rope:
The weight of the rope is given by the formula:

Weight of the rope = mass of the rope x acceleration due to gravity

Weight of the rope = 10 kg x 9.8 m/s^2

Weight of the rope = 98 N

The weight of the rope will act vertically downwards.

3. Tension force at the midpoint of the rope:
Let's assume that the tension force at the midpoint of the rope is T.

Now, if we consider the forces acting on the left half of the rope, the net force acting on it will be:

Net force = Force applied at one end - Tension force

Net force = 40 N - T

Similarly, if we consider the forces acting on the right half of the rope, the net force acting on it will be:

Net force = T - Weight of the rope

Net force = T - 98 N

As the rope is in equilibrium, the net force acting on both halves of the rope should be zero. Therefore, we can equate the two net forces:

40 N - T = T - 98 N

2T = 138 N

T = 69 N

Therefore, the tension at the midpoint of the rope is 69 N.

Answer: The correct option is (d) 5N.