Question

The dimension $ [ML^{-1} T^{-2}] $ is the physical quantity of

• A. Pressure \( \times \) Area
• B. Force \( \times \) Pressure
• C. Power \( \times \) Time
• D. Energy density

Hint:

Dimensions help identify the physical quantities. Always ensure that the product of the dimensions in the options matches the given dimension.

Answer 1

The Correct Option is D

The dimension \( [ML^{-1} T^{-2}] \) represents a quantity that involves mass, length, and time. To identify what physical quantity this dimension corresponds to, we can analyze the options:
1. Pressure \( \times \) Area: Pressure has the dimension \( [ML^{-1} T^{-2}] \), and Area has the dimension \( [L^2] \), so the product would have the dimension: \[ [ML^{-1} T^{-2}] \times [L^2] = [ML T^{-2}] \] This is not the same as \( [ML^{-1} T^{-2}] \), so this option is incorrect.
2. Force \( \times \) Pressure: Force has the dimension \( [ML T^{-2}] \), and Pressure has the dimension \( [ML^{-1} T^{-2}] \), so the product would have the dimension: \[ [ML T^{-2}] \times [ML^{-1} T^{-2}] = [M^2 T^{-4} L^{-1}] \] This is also not the same as \( [ML^{-1} T^{-2}] \), so this option is incorrect.
3. Power \( \times \) Time: Power has the dimension \( [ML^2 T^{-3}] \), and Time has the dimension \( [T] \), so the product would have the dimension: \[ [ML^2 T^{-3}] \times [T] = [ML^2 T^{-2}] \] This is not the same as \( [ML^{-1} T^{-2}] \), so this option is incorrect.
4. Energy Density: Energy has the dimension \( [ML^2 T^{-2}] \), and Density has the dimension \( [M L^{-3}] \), so the product (Energy Density) has the dimension: \[ [ML^2 T^{-2}] \times [ML^{-3}] = [ML^{-1} T^{-2}] \] This matches the given dimension \( [ML^{-1} T^{-2}] \), so the correct answer is Energy Density.
Thus, the physical quantity corresponding to \( [ML^{-1} T^{-2}] \) is Energy Density.