The units of $G$ are
$\begin{align*}\frac{\mathrm{m}^3}{\mathrm{kg}\;\mathrm{s}^2}\end{align*}$
The units of $\hbar$ are
$\begin{align*}\frac{\mathrm{kg}\;\mathrm{m}^2}{\text{s}}\end{align*}$
The units of $c$ are
$\begin{align*}\frac{\text{m}}{\text{s}}\end{align*}$
All three of the physical constants have a factor of $m$ raised to a power of 1 or higher in the numerator. Therefore, answers (A), (B), (C), and (D) must be wrong because they each have no denomonator and the sum of the exponents of the physical constants is greater than 1 in each case. Answer (E) can easily be seen to have units of $m$ if you plug in the above units for $G$ , $\hbar$ , and $c$ . Therefore, answer (E) is the only one that could be correct.

Solution to 1996 Problem 29