If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the

Q: If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is

d Say dimensional formale of mass is $H ^{ x } C ^{ y } G ^z$ $M ^1=\left( ML ^2 T ^{-1}\right)^{ x }\left( LT ^{-1}\right)\left( M ^{-1} L ^3 T ^{-2}\right)^Z$ $M ^1 L ^0 T ^0= M ^{ x - z } L ^{2 x + y +3 z} T ^{- x - y -2 z}$ on comparing both side $x-z=1$ $2 x+y+3 z=0$ $-x-y-2 z=0$ On solving above equations we get $x=\frac{1}{2} \quad y=\frac{1}{2} \quad z=\frac{-1}{2}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is

A$\left[h^{\frac{1}{2}} c^{-\frac{1}{2}} G^1\right]$
B$\left[ h ^1 c ^1 G ^{-1}\right]$
C$\left[ h ^{-\frac{1}{2}} c ^{\frac{1}{2}} G ^{\frac{1}{2}}\right]$
D$\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]$

JEE MAIN 2023, Diffcult

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

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