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1.Units, Dimensions and Measurement
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In a new system of units energy $(E)$, density $(d)$ and power $(P)$ are taken as fundamental units, then the dimensional formula of universal gravitational constant $G$ will be .......
A
$\left[E^{-1} d^{-2} P^2\right]$
B
$\left[E^{-2} d^{-1} P^2\right]$
C
$\left[E^2 d^{-1} P^{-1}\right]$
D
$\left[E^{-1} d^{-2} P^{-2}\right]$
Solution
(b)
$G=\left[E^g d^b P^c\right]$
$E=\left[M^2 T^{-2}\right]$
$d=\left[ ML ^{-3}\right]$
$P=\left[ ML ^2 T ^{-3}\right]$
$G=\left[M^{-1} L^3 T^{-2}\right]$
$\left[ M ^{-1} L ^3 T ^{-2}\right]=\left[ ML ^2 T ^{-2}\right]^a\left[ ML ^{-3}\right]^b\left[ ML ^2 T ^{-3}\right]^c$
$a+b+c=-1$
$2 a-3 b+2 c=3$
$-2 a-3 c=-2 \Rightarrow 2 a+3 c=2$
On solving.
$a=-2$
$b=-1$
$c=2$
So, $G=\left[E^{-2} d^{-1} P^2\right]$
Standard 11
Physics
