The characteristic distance at which quantum gravitational effects are significant, the Planck length, can…

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $\mathrm{G}, \mathrm{h}$ and $\mathrm{c}$. Which of the following correctly gives the Planck length?
  1. $\mathrm{G}^2 \mathrm{hc}$
  2. $\left(\frac{\mathrm{Gh}}{\mathrm{c}^3}\right)^{\frac{1}{2}}$
  3. $\mathrm{G}^{\frac{1}{2}} \mathrm{~h}^2 \mathrm{c}$
  4. $G\left(h^2 \mathrm{c}^3\right.$

Solution

Plank length is a unit of length, $ \begin{aligned} &l_p=1.616229 \times 10^{-35} \mathrm{~m} \\ &l_p=\sqrt{\frac{h G}{c^3}} \end{aligned} $

Asked in: JEE Main 2018 (15 Apr Shift 2 Online)

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