Question

Simplify the following expression in terms of the dimensions mass, length, and time given by [m], [l], and [t].

Answer 1

The dimensions of the quantities on the left-hand side of the given equations are determined. Each equation is analyzed, and the dimensions of force, kinetic energy, momentum, work, and angular momentum are found.

Step-by-step explanation:

In this question, we are given the dimensions of the physical quantities: mass [M], length [L], and time [T]. We are asked to determine the dimensions of the quantities on the left-hand side of the given equations. Let's analyze each equation:

1. F = ma: The dimensions of force [F] are given by [F] = [M] · [a] = MLT-2.
2. K = 0.5mv²: The dimensions of kinetic energy [K] are given by [K] = [M] · [v²] = [M] · (LT-1)² = [M] · L²T-2.
3. p = mv: The dimensions of momentum [p] are given by [p] = [M] · [v] = [M] · LT-1.
4. W = mas: The dimensions of work [W] are given by [W] = [M] · [a] · [s] = [M] · (LT-2) · [L] = ML²T-2.
5. L = mvr: The dimensions of angular momentum [L] are given by [L] = [M] · [v] · [r] = [M] · LT-1 · [L] = ML²T-1.

By analyzing the dimensions of each quantity in the equations, we can determine that the dimensions of the quantities on the left-hand side of the equations are as follows:

1. Dimensions of F = MLT-2.
2. Dimensions of K = ML²T-2.
3. Dimensions of p = MLT-1.
4. Dimensions of W = ML²T-2.
5. Dimensions of L = ML²T-1.