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1.Units, Dimensions and Measurement
hard
If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density
A
$\left[{FL}^{-4} {T}^{2}\right]$
B
$\left[{FL}^{-3} {T}^{2}\right]$
C
$\left[{FL}^{-5} {T}^{2}\right]$
D
$\left[{FL}^{-3} {T}^{3}\right]$
(JEE MAIN-2021)
Solution
$\text { Density }=\left[{F}^{{a}} {L}^{{b}} {T}^{{c}}\right]$
${\left[{ML}^{-3}\right]=\left[{M}^{{a}} {L}^{{a}} {T}^{-2 {a}} {L}^{{b}} {T}^{{c}}\right]}$
${\left[{M}^{1} {L}^{-3}\right]=\left[{M}^{{a}} {L}^{{a}+{b}} {T}^{-2 {a}+c}\right]}$
${a}=1 ; \quad {a}+{b}=-3 \quad ; \quad-2 {a}+{c}=0$
$\quad 1+{b}=-3 \quad {c}=2 {a}$
${b}=-4 \quad {c}=2$
So, density $=\left[{F}^{1} {L}^{-4} {T}^{2}\right]$
Standard 11
Physics
