1. **State the problem:** We have a retarding force $F$ acting on a sphere moving with velocity $V$. The force is given by the equation $$F = K r V,$$ where $r$ is the radius of the sphere and $K$ is a constant. We need to find the SI unit of $K$ in terms of other SI units. 2. **Identify the units of each quantity:** - Force $F$ has SI unit newton (N), where $$1\ \text{N} = 1\ \text{kg} \cdot \text{m/s}^2.$$ - Radius $r$ has SI unit meter (m). - Velocity $V$ has SI unit meter per second (m/s). 3. **Express the units in the equation:** $$[F] = [K][r][V].$$ Substitute the units: $$\text{N} = [K] \times \text{m} \times \frac{\text{m}}{\text{s}} = [K] \times \frac{\text{m}^2}{\text{s}}.$$ 4. **Solve for the unit of $K$:** $$[K] = \frac{\text{N}}{\frac{\text{m}^2}{\text{s}}} = \text{N} \times \frac{\text{s}}{\text{m}^2}.$$ 5. **Substitute the unit of newton:** $$[K] = \left(\text{kg} \cdot \frac{\text{m}}{\text{s}^2}\right) \times \frac{\text{s}}{\text{m}^2} = \text{kg} \times \frac{\text{m}}{\text{s}^2} \times \frac{\text{s}}{\text{m}^2} = \text{kg} \times \frac{1}{\text{m} \cdot \text{s}}.$$ 6. **Final unit of $K$:** $$[K] = \frac{\text{kg}}{\text{m} \cdot \text{s}}.$$ This means the SI unit of $K$ is kilogram per meter-second.