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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
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 $G, h$ and $c$ . Which of the following correctly gives the Planck length?
  • A
    $G^2hc$
  • ✓
    ${\left( {\frac{{Gh}}{{{c^3}}}} \right)^{\frac{1}{2}}}$
  • C
    ${G^{\frac{1}{2}}}{h^2}c$
  • D
    $Gh^2c^3$
✓

Answer

Correct option: B.
${\left( {\frac{{Gh}}{{{c^3}}}} \right)^{\frac{1}{2}}}$
b
Plank length is a unit of length

$I_p\,= 1.616229\times10^{-35}\,m$

${l_p} = \sqrt {\frac{{hG}}{{{c^3}}}} $

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