If force ({F}) , length ({L}) and time ({T}) are taken as fundamental quantities. Then what will be

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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

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