Question

Consider the physical quantities m, s, v, a, t, and r with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, [t] = T, and [r] = L. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation:

(a) F = ma;
(b) K = 0.5mv2;
(c) p = mv;
(d) W = mas;
(e) L = mvr.

Answer 1

The left-hand side of equation (a) has dimensions [F] = MLT-2. The left-hand side of equation (b) has dimensions [K] = ML2T-2. The left-hand side of equation (c) has dimensions [p] = MLT-1.

Step-by-step explanation:

(a) F = ma:

The left-hand side, which is force, has dimensions [F] = MLT-2.

(b) K = 0.5mv2:

The left-hand side, which is kinetic energy, has dimensions [K] = ML2T-2.

(c) p = mv:

The left-hand side, which is momentum, has dimensions [p] = MLT-1.

(d) W = mas:

The left-hand side, which is work, has dimensions [W] = ML2T-2.

(e) L = mvr:

The left-hand side, which is angular momentum, has dimensions [L] = ML2T-1.