If force ({F}), length ({L}) and time ({T}) a | vedclass

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Question

$	ext { Density }=\left[{F}^{{a}} {L}^{{b}} {T}^{{c}}ight]$

${\left[{ML}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}} {T}^{-2 {a}} {L}^{{b}} {T}^{{c}}\

Vedclass · Accepted Answer

$\left[{FL}^{-4} {T}^{2}\right]$

Vedclass · Answer

$	ext { Density }=\left[{F}^{{a}} {L}^{{b}} {T}^{{c}}ight]$

${\left[{ML}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}} {T}^{-2 {a}} {L}^{{b}} {T}^{{c}}ight]}$

${\left[{M}^{1} {L}^{-3}ight]=\left[{M}^{{a}} {L}^{{a}+{b}} {T}^{-2 {a}+c}ight]}$

${a}=1 ; \quad {a}+{b}=-3 \quad ; \quad-2 {a}+{c}=0$

$\quad 1+{b}=-3 \quad {c}=2 {a}$

${b}=-4 \quad {c}=2$

So, density $=\left[{F}^{1} {L}^{-4} {T}^{2}ight]$

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

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