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JEE Main202131 Aug 2021Morning ShiftPhysicsUnits and DimensionsActual

Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, θ = angle, ρ = density , a , r = radius, g = the acceleration due to gravity, V = volume, p = pressure, W = work done, τ = torque, ϵ = permittivity, E = electric field, J = current density, L = length.

Options

  1. AW = τ θ
  2. BV = π p a 4 8 η L
  3. Ch = 2 scos θ ρ r g
  4. DJ = ϵ ∂ E ∂ t

Correct answer

B. V = π p a 4 8 η L

Step-by-step solution

Dimensions of π p a 4 8 η L (volume flow rate) is L 3   T – 1 .

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