Which of the following is the correct dimensional formula for energy? (2023)

Which of the following is the correct dimensional formula for energy? (2023)

Step 1: Understand that energy is related to work done.
Step 2: Know that work is defined as force times distance.
Step 3: Recall the formula for force, which is mass times acceleration (F = m * a).
Step 4: Recognize that acceleration can be expressed as distance over time squared (a = L/T^2).
Step 5: Substitute the expression for acceleration into the force formula: F = m * (L/T^2).
Step 6: This gives us the formula for force: F = M * (L/T^2) = M * L * T^-2.
Step 7: Now, substitute this force formula back into the work formula: Work = Force * Distance = (M * L * T^-2) * L.
Step 8: Simplify the work formula: Work = M * L^2 * T^-2.
Step 9: Since energy is equal to work, the dimensional formula for energy is the same: [M^1 L^2 T^-2].

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