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

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

Options:

  1. [M^1 L^2 T^-2]
  2. [M^1 L^1 T^-1]
  3. [M^0 L^2 T^-1]
  4. [M^2 L^1 T^-2]

Correct Answer: [M^1 L^2 T^-2]

Exam Year: 2023

Solution:

Energy has the dimensional formula [M^1 L^2 T^-2], as it is defined as work done, which is force times distance.

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

Practice Questions

Q1
Which of the following is the correct dimensional formula for energy? (2023)
  1. [M^1 L^2 T^-2]
  2. [M^1 L^1 T^-1]
  3. [M^0 L^2 T^-1]
  4. [M^2 L^1 T^-2]

Questions & Step-by-Step Solutions

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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