Question

The term (ηs/τ) (η = coefficient of viscosity, s = surface tension, τ = torque), would become dimensionally compatible with a term obtained by multiplying, G, (the universal gravitational constant) with another quantity, having the dimensions of

(1) (Velocity) x (pressure)

(2) Time x (density)²

(3) Frequency x (force)

(4) Momentum / (acceleration)²

Answer 1

(2) Time x (density)²

We have,

∴ The required multiplier is [M²L^-6T]

This equals time × (density)2 because the dimensional of this term are (T) × (ML^-3)² = [M²L^-6T], which are the required dimensions.