The damping force on an oscillator is directly proportional to the velocity .The units of the constant of proportionality are

Options

A. `kgs`
B. `kgms^(-1)`
C. `kgms^(-2)`
D. `kgs^(-1)`

Explanation

To solve the problem, we need to determine the units of the constant of proportionality (k) in the damping force equation where the damping force (F) is directly proportional to the velocity (v).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The damping force (F) is given to be directly proportional to the velocity (v). Mathematically, this can be expressed as:
\[ F = k \cdot v \]
where \( k \) is the constant of proportionality.

2. **Rearranging the Equation**:
To find the units of \( k \), we can rearrange the equation:
\[ k = \frac{F}{v} \]

3. **Identifying the Units**:
- The unit of force (F) in the International System of Units (SI) is Newton (N).
- The unit of velocity (v) is meters per second (m/s).

4. **Substituting the Units**:
Now, substituting the units into the equation for \( k \):
\[ k = \frac{\text{N}}{\text{m/s}} \]

5. **Converting Units**:
We know that 1 Newton (N) can be expressed in terms of base units:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]
Therefore, substituting this into our equation for \( k \):
\[ k = \frac{1 \text{ kg} \cdot \text{m/s}^2}{\text{m/s}} = \frac{1 \text{ kg} \cdot \text{m/s}^2 \cdot \text{s}}{\text{m}} \]

6. **Simplifying the Units**:
The meters (m) in the numerator and denominator cancel out:
\[ k = \frac{1 \text{ kg}}{\text{s}} \]

7. **Final Result**:
Thus, the units of the constant of proportionality \( k \) are:
\[ \text{kg/s} \]

### Conclusion:
The units of the constant of proportionality \( k \) in the damping force equation are \( \text{kg/s} \).

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