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A body is in motion inside a liquid, and the viscous resistive force on it is directly proportional to its speed. What are the dimensions of the proportionality constant?

1. [ML⁻¹T⁻¹]
2. [MLT⁻¹]
3. [M⁰LT⁻¹]
4. [ML⁰T⁻¹]

Correct answer: [ML⁰T⁻¹]

Solution

The proportionality constant relates the viscous force to speed, which means it must have dimensions that allow the equation to balance. Since the resistive force has dimensions of [MLT⁻²] and speed has dimensions of [LT⁻¹], the proportionality constant must have dimensions of [ML⁰T⁻¹] to ensure the units are consistent.

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