Solution: Work has the dimensional formula [M^1 L^2 T^-2].
Steps: 8
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: Distance / Time.
Step 5: Therefore, acceleration has the dimensional formula: [L^1 T^-2].
Step 6: Now, substitute the dimensional formulas into the force formula: 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 force's dimensional formula by distance's dimensional formula, 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].
