Question: The dimensional formula for energy is: (2020)
Options:
[M^1 L^2 T^-2]
[M^2 L^1 T^-2]
[M^0 L^2 T^0]
[M^1 L^0 T^-1]
Correct Answer: [M^1 L^2 T^-2]
Exam Year: 2020
Solution:
Energy is defined as work done, which has the dimensional formula [M^1 L^2 T^-2].
The dimensional formula for energy is: (2020)
Practice Questions
Q1
The dimensional formula for energy is: (2020)
[M^1 L^2 T^-2]
[M^2 L^1 T^-2]
[M^0 L^2 T^0]
[M^1 L^0 T^-1]
Questions & Step-by-Step Solutions
The dimensional formula for energy is: (2020)
Step 1: Understand that energy is defined as work done.
Step 2: Recall the formula for work done, which is Work = Force × Distance.
Step 3: Know that Force is defined as mass times acceleration (Force = Mass × Acceleration).
Step 4: The dimensional formula for mass is [M^1].
Step 5: The dimensional formula for acceleration is [L^1 T^-2] (since acceleration is change in velocity over time).
Step 6: Combine the dimensional formulas for Force: [M^1] × [L^1 T^-2] = [M^1 L^1 T^-2].
Step 7: Now, substitute this back into the work formula: Work = Force × Distance.
Step 8: The dimensional formula for distance is [L^1].
Step 9: Combine the dimensional formulas for work: [M^1 L^1 T^-2] × [L^1] = [M^1 L^2 T^-2].
Step 10: Therefore, the dimensional formula for energy is [M^1 L^2 T^-2].
Dimensional Analysis – Understanding how physical quantities can be expressed in terms of basic dimensions such as mass (M), length (L), and time (T).
Energy and Work – Recognizing that energy is defined as the capacity to do work, and that work has a specific dimensional formula.
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