If pressure P, velocity V and time T are taken as fundamental units, then the dimensional formula of force is:

Model Answer & Options

Source: Extra Practice

[P V² T²]

[P V T²]

[P V² T]

[P⁻¹ V² T²]

Explanation

Let F = [P^a V^b T^c]. [MLT⁻²] = [ML⁻¹T⁻²]^a [LT⁻¹]^b [T]^c. Equating powers of M: a = 1. Equating powers of L: -a + b = 1 => -1 + b = 1 => b = 2. Equating powers of T: -2a - b + c = -2 => -2(1) - 2 + c = -2 => c = 2. So F = [P V² T²]. Other options fail the dimensional consistency check for mass, length, or time.

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