Question 112: Units , Dimensions and Error Analysis

Question

Match List I with List II

LIST I 
 LIST II

A.
Angular momentum
I.
$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$

B.
Torque
II.
$\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$

C.
Stress
III
$\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$

D.
Pressure gradient
IV.
$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below:

Accepted Answer

$\vec{L}=\vec{r} 	imes \vec{p} \Rightarrow[\mathrm{L}]=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{0}ight]\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}ight]$
$$
=\left[\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1}ight]
$$
$$
\begin{aligned}
\vec{	au}=\vec{r} 	imes \vec{F} \Rightarrow[	au] & =\left[\mathrm{L}^{1}ight]\left[\mathrm{MLT}^{-2}ight] \\
& =\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}ight]
\end{aligned}
$$
Stress $\equiv$ Pressure $=\frac{F}{A} \Rightarrow[$ Stress $]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}ight]$
Pressure Gradient $=\frac{d P}{d x} \Rightarrow[$ Pressure Gradient $]$

$$
=\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}ight]
$$

Answer

A - I, B - IV, C - III, D - II

Answer

A - III, B - I, C - IV, D - II

Answer

A - IV, B - II, C - I, D - III

Answer

A - II, B - III, C - IV, D - I

Units , Dimensions and Error Analysis

Choose the correct answer: