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

Q: 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 .......

b (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, $G=\left[E^{-2} d^{-1} P^2\right]$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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$\left[E^{-1} d^{-2} P^{-2}\right]$

Medium

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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