Explanation:

The given problem involves a car moving in a circular horizontal track with a constant speed and a plumb bob suspended from the roof of the car by a string. We need to find the angle made by the string with the vertical.

To solve this problem, we can consider the forces acting on the plumb bob. There are two forces acting on the plumb bob: the tension in the string and the gravitational force.

Forces acting on the plumb bob:
1. Tension in the string: The tension in the string acts along the direction of the string and prevents the plumb bob from falling.
2. Gravitational force: The gravitational force acts vertically downwards.

Equilibrium condition:
Since the plumb bob is in equilibrium, the net force acting on it must be zero. This implies that the tension in the string must be equal and opposite to the gravitational force.

Resolving the forces:
Let's resolve the gravitational force into two components:
1. The component along the string: This component opposes the tension in the string.
2. The component perpendicular to the string: This component does not affect the tension in the string.

Calculating the angle:
Since the plumb bob is in equilibrium, the component of the gravitational force along the string must be equal to the tension in the string.

Using trigonometry, we can calculate the angle made by the string with the vertical. Let's denote this angle as θ.

Sin(θ) = (Component of gravitational force along the string) / (Magnitude of gravitational force)
Sin(θ) = (mg) / (mg)
Sin(θ) = 1

To find the value of θ, we can take the inverse sine (sin^-1) of both sides.

θ = sin^-1(1)
θ = 90°

Therefore, the angle made by the string with the vertical is 90 degrees or a right angle.

Conclusion:
The plumb bob hangs vertically downwards due to the equilibrium of forces. The string makes a right angle with the vertical.

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