Step 1: Understand that force is defined by Newton's second law of motion, which states that force equals mass times acceleration (F = m * a).
Step 2: Identify the dimensions of mass (m). Mass has the dimensional formula [M^1], where M represents mass.
Step 3: Identify the dimensions of acceleration (a). Acceleration is defined as the change in velocity over time. Velocity has the dimensional formula [L^1 T^-1] (length over time).
Step 4: Since acceleration is the change in velocity over time, its dimensional formula is [L^1 T^-2] (length per time squared).
Step 5: Combine the dimensional formulas for mass and acceleration to find the dimensional formula for force. This is done by multiplying the two formulas: [M^1] * [L^1 T^-2].
Step 6: The result of the multiplication gives us the dimensional formula for force: [M^1 L^1 T^-2].
