the correct form of Stroke`s law is (symbols have their usual meanings)

Options

A. `vecF=-6pietaavecv`
B. `vecF=6pietaavecv`
C. `vecF=-4pietaavecv`
D. `vecF=4pietaavecv`

Answer

**Step-by-Step Solution:**

1. **Understanding Stokes' Law**: Stokes' Law describes the force of viscosity acting on a spherical object moving through a viscous fluid. It states that the viscous drag force (F) acting on the sphere is directly proportional to the radius of the sphere (r), the velocity of the sphere (v), and the viscosity of the fluid (η).

2. **Identifying the Variables**:
- Let \( F \) be the viscous drag force.
- Let \( r \) be the radius of the sphere.
- Let \( v \) be the velocity of the sphere.
- Let \( \eta \) be the coefficient of viscosity of the fluid.

3. **Formulating Stokes' Law**: According to Stokes' Law, the magnitude of the viscous drag force can be expressed as:
\[ F = 6 \pi \eta r v \]
This equation indicates that the force is proportional to the radius of the sphere, the viscosity of the fluid, and the velocity of the sphere.

4. **Considering Direction**: The direction of the viscous drag force is opposite to the direction of the velocity of the sphere. Therefore, in vector form, Stokes' Law can be expressed as:
\[ \vec{F} = -6 \pi \eta r \vec{v} \]
Here, the negative sign indicates that the drag force acts in the opposite direction to the velocity vector.

5. **Conclusion**: The correct form of Stokes' Law is:
\[ \vec{F} = -6 \pi \eta r \vec{v} \]

**Final Answer**: The correct form of Stokes' Law is \( \vec{F} = -6 \pi \eta r \vec{v} \).

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