JEE Main 201815 AprilEvening ShiftOnline

Exam: JEE Main
Year: 2018
Date: 15 April
Shift: Evening Shift
Mode: Online
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Units and Dimensions

The characteristic distance at which quantum gravitational effects...

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?

Options

A $\mathrm{G}^2 \mathrm{hc}$
B $\left(\frac{\mathrm{Gh}}{\mathrm{c}^3}\right)^{\frac{1}{2}}$
C $\mathrm{G}^{\frac{1}{2}} \mathrm{~h}^2 \mathrm{c}$
D $G\left(h^2 \mathrm{c}^3\right.$

Correct answer

B. $\left(\frac{\mathrm{Gh}}{\mathrm{c}^3}\right)^{\frac{1}{2}}$

Step-by-step solution

Plank length is a unit of length,

\begin{aligned}&l_p=1.616229 \times10^{-35} \mathrm{~m}\\ &l_p=\sqrt{\frac{h G}{c^3}} \end{aligned}

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