The dimensional formula of an expression can be obtained by analyzing the dimensions of the involved variables. Let's break down the given expression, (1/2)mv^2 + ma, and determine its dimensional formula step by step:
The first term, (1/2)mv^2, represents the kinetic energy of an object. The dimensional formula for kinetic energy is given by [M][L]^2[T]^-2, where [M] represents mass, [L] represents length or distance, and [T] represents time.
The second term, ma, represents the product of mass and acceleration. The dimensional formula for this term is [M][L][T]^-2.
Adding both terms together, we get:
(1/2)mv^2 + ma = [M][L]^2[T]^-2 + [M][L][T]^-2
Simplifying this expression, we find:
[M][L]^2[T]^-2 + [M][L][T]^-2 = [M][L][T]^-2 + [M][L][T]^-2 = [M][L][T]^-2
Therefore, the dimensional formula of (1/2)mv^2 + ma is [M][L][T]^-2, representing the dimensions of mass, length, and time.