KEY2PHYSICS

Consider the physical quantities m, s, v, a, and t with dimensions \([m] = M,\; [s] = L,\; [v] = LT^{–1}, \;[a] = LT^{–2}, \text{ and } [t] = T\).

Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation:

\(F = ma\)

\([F]=LT^{-2}\)

\([F]=MLT^{-1}\)

\([F]=ML^{-2}\)

\([F]=MLT^{-2}\)

\(K = 0.5mv^2\)

\([K]=ML^2T\)

\([K]=ML^2T^{-2}\)

\([K]=L^2T^{-2}\)

\([K]=MLT^{-2}\)

\(p = mv\)

\([P]=MLT\)

\([P]=ML^2T^{-1}\)

\([P]=MLT^{-1}\)

\([P]=M^2LT^{-1}\)

\(W = mas\)

\([W]=L^2M^{-2}\)

\([W]=ML^2T^{-2}\)

\([W]=ML^2T\)

\([W]=ML^{-2}T^{-1}\)

\(L = mvr\)

\([L]=M^{-2}L^2T^{-1}\)

\([L]=MLT^{-2}\)

\([L]=ML^2T^{-1}\)

\([L]=M^2LT^{-1}\)