If v is the velocity of the bob the force that is responsible for decrease of amplitude is proportional to

Options

A. `v^(2)`
B. `v`
C. `(1)/(v)`
D. `(1)/(v^(2))`

Explanation

To solve the question, we need to analyze the forces acting on the bob of a simple pendulum and understand how these forces relate to the decrease in amplitude of its oscillation.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a simple pendulum with a bob of mass \( m \) hanging from a string of length \( l \). The bob oscillates back and forth around the mean position.

2. **Identifying Forces**:
- As the bob moves, it experiences a resistive force due to air resistance or drag. This force acts opposite to the direction of motion of the bob.

3. **Expression for Drag Force**:
- The drag force \( F_d \) acting on a spherical object moving through a fluid (like air) can be expressed using Stokes' law:
\[ F_d = 6 \pi \eta v r \]
where:
- \( \eta \) is the coefficient of viscosity of the fluid,
- \( v \) is the velocity of the bob,
- \( r \) is the radius of the bob.

4. **Proportionality of Drag Force**:
- From the expression for drag force, we can see that the drag force \( F_d \) is directly proportional to the velocity \( v \) of the bob. This means:
\[ F_d \propto v \]

5. **Conclusion**:
- The force responsible for the decrease in amplitude of the pendulum's oscillation, which is the drag force, is thus proportional to the velocity \( v \) of the bob.

### Final Answer:
The force that is responsible for the decrease of amplitude is proportional to the velocity \( v \) of the bob.

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