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1.Units, Dimensions and Measurement
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If force $(F)$, velocity $(V)$ and time $(T)$ are considered as fundamental physical quantity, then dimensional formula of density will be:
A$FV ^{-2} T ^2$
B$FV ^{-4} T ^{-2}$
C$FV ^4 T ^{-6}$
D$F ^2 V ^{-2} T ^6$
(JEE MAIN-2023)
Solution
${\left[ ML ^{-3}\right]=\left[ MLT ^{-2}\right]^{ a }\left[ LT ^{-1}\right]^{ b }[ T ]^{ c }}$
$=\left[ M ^{ a } L ^{ a + b } T ^{-2 a – b + c }\right]$
$a =1$
$a + b =-3$
$\Rightarrow b =-4$
also $-2 a-b+c=0$
$c =-2$
$=\left[ M ^{ a } L ^{ a + b } T ^{-2 a – b + c }\right]$
$a =1$
$a + b =-3$
$\Rightarrow b =-4$
also $-2 a-b+c=0$
$c =-2$
Standard 11
Physics
