Question

If the dimensions of length are expressed as \( G^x c^y \hbar^z \), where \( G \), \( c \) and \( \hbar \) are gravitational constant, speed of light and Planck’s constant respectively, then

• A. \( x=\frac12,\; y=\frac12 \)
• B. \( x=\frac12,\; z=\frac12 \)
• C. \( y=\frac12,\; z=\frac32 \)
• D. \( y=\frac32,\; z=\frac12 \)

Hint:

Planck scale: \begin{itemize} \item Planck length uses \( \sqrt{\frac{G\hbar}{c^3}} \). \end{itemize}

Answer 1

The Correct Option is B