The characteristics distance at which quantum gravitational effects are significant, the plank length, can be determined from a suitable combination of the fundamental physical constants G,h and c. Which of the following correctly gives the plank length?

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$G^{2} h c$

${(\frac{G h}{c^{3}})}^{\frac{1}{2}}$

$G^{\frac{1}{2}} h^{2} c$

$G h^{2} c^{3}$

answer is B.

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Detailed Solution

$Planck Length dimension [L^{1}]$

$Velocity dimension [L^{1} T^{- 1}]$

$Planck constant dimension [{ML}^{2} T^{- 1}]$

$Gravitational constant dimension [M^{- 1} L^{3} T^{- 1}]$

${So l}_{p} = \sqrt{\frac{hG}{c^{3}}}$ , $where l_{p} is plank' s length$

$Putting all dimension in formula we get length as answer.$

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