Stoke's theorem is applicable only to

Options

A. non-viscous liquids
B. viscous liquids
C. solutions
D. pure metals

Answer

**Step-by-Step Solution:**

1. **Understanding Stokes' Theorem**: Stokes' Theorem relates to the behavior of objects moving through a viscous fluid. It describes the drag force experienced by a spherical object moving through such a fluid.

2. **Identifying the Drag Force**: According to Stokes' Theorem, the formula for the drag force (Fd) acting on a spherical object in a viscous fluid is given by:
\[ F_d = 6 \pi \eta r v \]
where:
- \( \eta \) is the dynamic viscosity of the fluid,
- \( r \) is the radius of the sphere,
- \( v \) is the velocity of the object relative to the fluid.

3. **Conditions for Applicability**: Stokes' Theorem is specifically applicable under certain conditions:
- The fluid must be viscous, meaning it has a significant internal friction that affects the motion of objects through it.
- The object must be spherical for the theorem to apply directly.

4. **Exclusions**: Stokes' Theorem does not apply to:
- Non-viscous fluids, where internal friction is negligible.
- Pure metals or solutions, as they do not exhibit the same drag characteristics as viscous fluids.

5. **Conclusion**: Therefore, Stokes' Theorem is applicable only to viscous fluids.

**Final Answer**: Stokes' Theorem is applicable only to viscous fluids.

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