The viscous drag on a spherical body moving with a speed v is proportional to

Options

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

Answer

To solve the question regarding the viscous drag on a spherical body moving with a speed \( v \), we can refer to Stokes' Law. Here’s a step-by-step solution:

### Step 1: Understand Stokes' Law
Stokes' Law states that the viscous drag force \( F \) experienced by a spherical object moving through a viscous fluid is given by the equation:
\[ F = 6 \pi \eta r v \]
where:
- \( F \) is the viscous drag force,
- \( \eta \) is the dynamic viscosity of the fluid,
- \( r \) is the radius of the sphere,
- \( v \) is the velocity of the sphere.

### Step 2: Identify the Proportionality
From the equation, we can see that the viscous drag force \( F \) is directly proportional to the velocity \( v \) of the spherical body. This means:
\[ F \propto v \]

### Step 3: Conclusion
Thus, the viscous drag on a spherical body moving with a speed \( v \) is proportional to \( v \).

### Final Answer
The viscous drag on a spherical body moving with a speed \( v \) is proportional to \( v \).

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