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The force F on a sphere of radius ‘a’ is moving in a medium with velocity v is given by F = 6πηav. The dimensions of η are

1. [ML⁻¹T⁻¹]
2. [ML⁻²]
3. [ML⁻¹]
4. [ML⁻¹T⁻¹]

Correct answer: [ML⁻¹T⁻¹]

Solution

The given formula F = 6πηav relates force (F) to velocity (v) and radius (a). Rearranging for η, we get η = F / (6πav). Since F has dimensions [MLT⁻²], a has dimensions [L], and v has dimensions [LT⁻¹], the dimensions of η are [MLT⁻²] / ([L][LT⁻¹]) = [ML⁻¹T⁻¹].

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