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:

$F = ma$

$[F]=MLT^{-2}$

$[F]=LT^{-2}$

$[F]=ML^{-2}$

$[F]=MLT^{-1}$

$K = 0.5mv^2$

$[K]=ML^2T$

$[K]=ML^2T^{-2}$

$[K]=MLT^{-2}$

$[K]=L^2T^{-2}$

$p = mv$

$[P]=MLT$

$[P]=M^2LT^{-1}$

$[P]=MLT^{-1}$

$[P]=ML^2T^{-1}$

$W = mas$

$[W]=L^2M^{-2}$

$[W]=ML^{-2}T^{-1}$

$[W]=ML^2T$

$[W]=ML^2T^{-2}$

$L = mvr$

$[L]=ML^2T^{-1}$

$[L]=M^2LT^{-1}$

$[L]=MLT^{-2}$

$[L]=M^{-2}L^2T^{-1}$