Step 1: Understand that work is defined as force applied over a distance.
Step 2: Recall that force is calculated using the formula: Force = Mass × Acceleration.
Step 3: The dimensional formula for mass (M) is [M^1].
Step 4: The dimensional formula for acceleration is: Acceleration = Change in velocity / Time. Velocity has the formula: Velocity = Distance / Time.
Step 5: Therefore, the dimensional formula for acceleration is [L^1 T^-2] (since distance is [L^1] and time is [T^1]).
Step 6: Now, substitute the dimensional formula for force: Force = Mass × Acceleration = [M^1] × [L^1 T^-2] = [M^1 L^1 T^-2].
Step 7: Since work is force multiplied by distance, we need to multiply the dimensional formula for force by the dimensional formula for distance, which is [L^1].
Step 8: Therefore, the dimensional formula for work is: [M^1 L^1 T^-2] × [L^1] = [M^1 L^2 T^-2].
