An expression for buoyant force is FB = ρgV, where FB has dimensions [MLT−2], ρ has dimensions [ML−3], and g has dimensions [LT−2]. What must be the dimensions of V? If someone can show how they got the answer it would be appreciated!
Here are the possible answers: [L^3], [L]^-1[T], [L][T]^-1, [M][L]^-4, [L^-3]
Here are the possible answers: [L^3], [L]^-1[T], [L][T]^-1, [M][L]^-4, [L^-3]
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V = (FB) / (ρg)
= MLT^(-2) / [ML^(-3) * LT^(-2)]
Now cancel out M, L and T^(-2) and you're left with 1 / L^(-3),
which is the same as L^3.
= MLT^(-2) / [ML^(-3) * LT^(-2)]
Now cancel out M, L and T^(-2) and you're left with 1 / L^(-3),
which is the same as L^3.