Length of the Simple Pendulum and Mass of the Bob

Given:
Length of the simple pendulum (L) = 2m
Mass of the bob (m) = 0.2kg

Tension in the String

It is given that if the tension in the string exceeds 4N, it will break.

Maximum Angle Made by the String with the Vertical

When the bob is whirled in a horizontal plane, it moves in a circular path. The tension in the string provides the necessary centripetal force to keep the bob moving in a circular path. The maximum angle made by the string with the vertical during rotation can be determined by analyzing the forces acting on the bob.

Forces Acting on the Bob

1. Weight (mg): The weight of the bob acts vertically downwards.
2. Tension (T): The tension in the string acts towards the center of the circular path.
3. Centripetal Force (Fc): The centripetal force acts towards the center of the circular path.

Analysis of Forces

At the maximum angle, the tension in the string will be at its maximum value without exceeding 4N.

1. At the maximum angle, the tension (T) and weight (mg) can be resolved into horizontal and vertical components.
2. The vertical component of the tension should be equal to the weight of the bob (mg) to maintain equilibrium in the vertical direction.
3. The horizontal component of the tension provides the necessary centripetal force to keep the bob moving in a circular path.

Equations

1. Vertical Component: T * cosθ = mg
2. Horizontal Component: T * sinθ = Fc

Solving the Equations

1. From equation 1, we can solve for T:
T = mg / cosθ

2. Substituting this value of T in equation 2, we get:
(mg / cosθ) * sinθ = Fc

3. Simplifying the equation, we have:
tanθ = Fc / mg

Calculating the Maximum Angle

To calculate the maximum angle made by the string with the vertical, we can substitute the given values in the equation and solve for θ.

tanθ = Fc / mg
tanθ = (mv²) / (mg)
tanθ = (m * (v² / g))
tanθ = (0.2 * (v² / 9.8))

Since the speed (v) of the bob is not given, we cannot calculate the exact value of the maximum angle without additional information. However, the equation provides a general relationship between the maximum angle and the speed of the bob.

Conclusion

To determine the maximum angle made by the string with the vertical during rotation of the bob in a horizontal plane, we need to know the speed of the bob. Without that information, we can only express the relationship between the maximum angle, speed, and other given parameters using the equation tanθ = (0.2 * (v² / 9.8)).

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