If the string of a pendulum were cut when the bob is at its central position, the bob would fall to the earth due to the absence of the

Options

A. force of buoyancy
B. force of deformation
C. force exerted by the string in the downward direction
D. force exerted by the string in the upward direction

Answer

To solve the question, "If the string of a pendulum were cut when the bob is at its central position, the bob would fall to the earth due to the absence of the...", we will analyze the forces acting on the bob of the pendulum when it is at the central position.

### Step-by-Step Solution:

1. **Understanding the Pendulum System**:
- A pendulum consists of a bob (mass) attached to a string. The other end of the string is fixed at a point.
- When the pendulum is at its central position (the lowest point), it is in equilibrium, meaning the forces acting on the bob are balanced.

2. **Forces Acting on the Bob**:
- At the central position, two main forces act on the bob:
- The gravitational force (weight) acting downward, which is \( mg \) (where \( m \) is the mass of the bob and \( g \) is the acceleration due to gravity).
- The tension force \( T \) exerted by the string acting upward.

3. **Equilibrium Condition**:
- In equilibrium at the central position, the tension in the string is equal to the weight of the bob:
\[ T = mg \]
- This means the net force acting on the bob is zero, and it remains at rest.

4. **Cutting the String**:
- If the string is cut while the bob is at the central position, the tension force \( T \) will no longer act on the bob.
- The only force acting on the bob will be its weight \( mg \), which acts downward.

5. **Resulting Motion**:
- Since the tension force is absent after the string is cut, the bob will experience a net downward force equal to its weight.
- Therefore, the bob will fall to the earth due to the absence of the upward tension force that was previously counteracting its weight.

6. **Conclusion**:
- The correct answer to the question is that the bob would fall to the earth due to the absence of the **force exerted by the string in the upward direction**.

### Final Answer:
The bob would fall to the earth due to the absence of the **force exerted by the string in the upward direction**.

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