Question 20: Units , Dimensions and Error Analysis

Question

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

Accepted Answer

To determine the physical quantity represented by the dimension $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$, let's analyze the dimensions of each of the given options step-by-step:
Option A: Pressure $$	imes$$ Area
Pressure has the dimension $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$ and Area has the dimension $$[\mathrm{L}^{2}]$$.
Thus:
$$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}] 	imes [\mathrm{L}^{2}] = [\mathrm{M L} \mathrm{~T}^{-2}]$$
This does not match $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$.
Option B: $$\mathrm{\frac{Force}{Pressure}}$$
Force has the dimension $$[\mathrm{MLT}^{-2}]$$ and Pressure has the dimension $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$.
Thus:
$$\mathrm{\frac{[\mathrm{MLT}^{-2}]}{[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]}} = [\mathrm{L}^{2}]$$
This does not match $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$.
Option C: Power $$	imes$$ Time
Power has the dimension $$[\mathrm{ML}^{2} \mathrm{~T}^{-3}]$$ and Time has the dimension $$[\mathrm{T}]$$.
Thus:
$$[\mathrm{ML}^{2} \mathrm{~T}^{-3}] 	imes [\mathrm{T}] = [\mathrm{ML}^{2} \mathrm{~T}^{-2}]$$
This does not match $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$.
Option D: Energy density
Energy density has the dimension $$[\mathrm{\frac{Energy}{Volume}}]$$.
Energy has the dimension $$[\mathrm{ML}^{2} \mathrm{~T}^{-2}]$$ and Volume has the dimension $$[\mathrm{L}^{3}]$$.
Thus:
$$\mathrm{\frac{[\mathrm{ML}^{2} \mathrm{~T}^{-2}]}{[\mathrm{L}^{3}]}} = [\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$
This matches $$[\mathrm{ML}^{-1} \mathrm{~T}^{-2}]$$.
Hence, the correct answer is:
Option D: Energy density

Answer

Pressure $$	imes$$ Area

Answer

$$\mathrm{\frac{Force}{Pressure}}$$

Answer

Power $$	imes$$ Time

Answer

Energy density

Units , Dimensions and Error Analysis

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

Choose the correct answer: