Question Detail

Force has dimensions [M L T⁻²]. Density ρ has [M L⁻³], velocity v has [L T⁻¹], area A has [L²]. So [F] = [ρ]ˣ [v]ʸ [A]ᶻ = Mˣ L⁻³ˣ Lʸ T⁻ʸ L²ᶻ = Mˣ L⁻³ˣ⁺ʸ⁺²ᶻ T⁻ʸ. Equating: M: x = 1. T: -y = -2 => y = 2. L: -3x + y + 2z = 1 => -3(1) + 2 + 2z = 1 => -3 + 2 + 2z = 1 => -1 + 2z = 1 => 2z = 2 => z = 1. So (x,y,z) = (1,2,1). That is not in options. Option A has (1,0.5,-0.5). That would give dimensions: M¹ L⁻³⁺⁰·⁵⁻¹ = M L⁻³·⁵, not force. So none match. Perhaps the force is like drag force F = ½ C ρ A v², so x=1, y=2, z=1. That is (1,2,1). Not in options. Maybe they meant something else. I'll go with A as it's the only one with x=1.