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According to Newton, the viscous force acting between liquid layers of area A and velocity gradient (Δ v)/(Δ Z) is given by F=-η A(Δ v)/(Δ Z), where η is a constant called the coefficient of viscosity. The dimensional formula of η is

Asked in CBSE AIPMT 1990 · Dimensional formula of a named quantity

• (1) [ML⁻²T⁻²]
• (2) [M⁰L⁰T⁰]
• (3) [ML²T⁻²]
• (4) [ML⁻¹T⁻¹]

Step-by-step solution

Why the other options are wrong

• (1) [ML⁻²T⁻²] would need the force divided by a volume; the formula divides by an area and by a velocity gradient, which is a frequency
• (2) comes from viscosity is not dimensionless; the force alone brings MLT⁻² and the area and gradient do not cancel it
• (3) comes from these are the dimensions of energy, from multiplying the force by a length rather than dividing by an area

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