The dimensional formula for work done

The dimensional formula for work done is derived as follows:

Work done is defined as the dot product of force and displacement. In other words, work done is the force applied on an object multiplied by the distance over which it is applied.

1. The dimensional formula of force (F) is [MLT^-2]. This is because force is mass times acceleration, and acceleration is length divided by time squared.

2. The dimensional formula of displacement (d) is [L]. This is because displacement is a distance, which is a measure of length.

3. Therefore, the dimensional formula for work done (W) is the product of the dimensional formulas for force and displacement.

So, W = F * d

Substituting the dimensional formulas for force and displacement, we get:

W = [MLT^-2] * [L]

Simplifying this, we get:

W = [ML^2T^-2]

So, the dimensional formula for work done is [ML^2T^-2].