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

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Answer & Solution

Correct Answer

(D) \(\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]\)

Step-by-step Solution

Detailed explanation

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

\(x=\frac{1}{2} \quad y=\frac{1}{2} \quad z=\frac{-1}{2}\)

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