Question:
If the dimensional formula of a physical quantity is $[M^1 L^2 T^{-2}]$, then the quantity is:
If the dimensional formula of a physical quantity is $[M^1 L^2 T^{-2}]$, then the quantity is:
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Work and all forms of energy (kinetic, potential, thermal, etc.) always share the exact same dimensional formula $[M^1 L^2 T^{-2}]$.
Updated On: Jun 3, 2026
- Force
- Work
- Power
- Momentum
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Dimensional formulas represent physical quantities in terms of the fundamental dimensions of mass ($M$), length ($L$), and time ($T$).
Step 2: Meaning
Work ($W$) is defined as the product of force ($F$) and displacement ($d$): $W = F \cdot d$.
Step 3: Analysis
Force has the dimensional formula: \[ [F] = [M^1 L^1 T^{-2}] \] Multiplying the dimensions of force by the dimensions of displacement ($[L^1]$) yields: \[ [W] = [M^1 L^1 T^{-2}] \times [L^1] = [M^1 L^2 T^{-2}] \] Comparing with other options: Force is $[M^1 L^1 T^{-2}]$, Power is $[M^1 L^2 T^{-3}]$, and Momentum is $[M^1 L^1 T^{-1}]$.
Step 4: Conclusion
Therefore, the dimensional formula $[M^1 L^2 T^{-2}]$ represents Work.
Final Answer: (B)
Dimensional formulas represent physical quantities in terms of the fundamental dimensions of mass ($M$), length ($L$), and time ($T$).
Step 2: Meaning
Work ($W$) is defined as the product of force ($F$) and displacement ($d$): $W = F \cdot d$.
Step 3: Analysis
Force has the dimensional formula: \[ [F] = [M^1 L^1 T^{-2}] \] Multiplying the dimensions of force by the dimensions of displacement ($[L^1]$) yields: \[ [W] = [M^1 L^1 T^{-2}] \times [L^1] = [M^1 L^2 T^{-2}] \] Comparing with other options: Force is $[M^1 L^1 T^{-2}]$, Power is $[M^1 L^2 T^{-3}]$, and Momentum is $[M^1 L^1 T^{-1}]$.
Step 4: Conclusion
Therefore, the dimensional formula $[M^1 L^2 T^{-2}]$ represents Work.
Final Answer: (B)
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