Problem statement:
A ball weighing 100N is suspended vertically by a string 5m long. Find the magnitude of the force which should be applied horizontally to hold the ball 1m above the lowest point. Also, determine the tension in the string.

Solution:
To solve this problem, we need to consider the forces acting on the ball and analyze the equilibrium conditions.

Forces acting on the ball:
- Weight of the ball (W): The ball weighs 100N and acts vertically downwards.
- Tension in the string (T): The string exerts a force on the ball in the vertical direction to balance the weight.

Equilibrium conditions:
For the ball to be held 1m above the lowest point, the net force acting on it must be zero in both the vertical and horizontal directions.

Horizontal equilibrium:
Since the ball is not moving horizontally, the net force in the horizontal direction is zero. Therefore, the magnitude of the force applied horizontally to hold the ball can be calculated using the equation:

Force (F) = T sinθ

Here, θ is the angle the string makes with the vertical direction. In this case, θ = 90° since the string is vertical. Therefore, sinθ = sin(90°) = 1.

Hence, F = T sinθ = T × 1 = T

To find the value of T, we need to consider the vertical equilibrium.

Vertical equilibrium:
For the ball to be at rest in the vertical direction, the net force acting on it must be zero. The forces acting vertically are the weight of the ball (W) and the tension in the string (T).

T - W = 0

Substituting the values, we get:

T - 100N = 0

Therefore, T = 100N

Conclusion:
The magnitude of the force that needs to be applied horizontally to hold the ball 1m above the lowest point is 100N. The tension in the string is also 100N.