Dimensional Analysis

Question 1

Question

${\rm What \ are \ the \ dimensions \ of \ velocity?}$

Answer

${\rm \frac{[Length]}{[Time]} }$
${\rm [Length] }$ - ${\rm [Time] }$
${\rm [Length] \ x \ [Time] }$
${\rm \frac{[Time]}{[Length} }$
${\rm {[Length]} \ + \ {[Time]} }$

Question 2

Question

${\rm Given}$

$E=mc^2,$

${\rm which \ of \ the \ below \ is \ the \ equivalent \ unit \ for \ the \ Joule?}$

Answer

${\rm kgm^2s^{-2} }$
${\rm kgm^2s^{-4} }$
${\rm kg^2m^2s^{-2} }$
${\rm kg^2m^2s^2 }$
${\rm kgm^3s^{-2} }$

Question 3

Question

${\rm The \ Boltzmann \ constant, \ } k_b {\rm \ is \ defined \ as \ } k_b = \frac{R}{N_0}, {\rm \ where \ } R {\rm \ is \ the \ gas \ constant \ with \ units \ Jmol^{-1}K^{-1}, \ and \ }$

$N_0 {\rm \ is \ Avagadro's \ constant \ with \ unit \ mol^{-1}. \ Using \ this \ information, \ what \ are \ the \ units \ of } \ k_b?$

Answer

${\rm JK^{-1} }$
${\rm JK }$
${\rm J^{-1}K^{-1} }$
${\rm JK^{-1}mol }$
${\rm JK^{-1}mol{-1} }$

Question 4

Question

${\rm The \ Coulomb \ constant \ is \ defined \ as \ } k = \frac{1}{4\pi\epsilon_0} {\rm What \ is \ the \ value \ of \ } \ k?$

$\epsilon_0=8.85 {\rm \ x \ }10^{-12} {\rm \ C^2N^{-1}m^{-2} }$

Answer

${\rm 8.987 \ x \ 10^9 \ Nm^2C^{-2} }$
${\rm 8.987 \ x \ 10^9 \ NC^2m^2 }$
${\rm 8.987 \ x \ 10^9 }$
${\rm 8.987 \ x \ 10^9 \ C^2N^{-1}m^{-2} }$
${\rm 8.987 \ x \ 10^9 \ C^{-2}N^{-1}m^{-2} }$

Question 5

Question

${\rm Given \ } \rho = \frac{m}{V} {\rm \ what \ are \ the \ units \ of \ } \rho {\rm?}$

Answer

${\rm kgm^{-3} }$
${\rm kgm^3 }$
${\rm kg^{-1}m^3 }$
${\rm kgm^{-1} }$
${\rm kg^{-1}m^{-3} }$

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Dimensional Analysis

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Resource summary

Question 1

Question 2

Question 3

Question 4

Question 5

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	Created by Jackie Grant over 8 years ago