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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Units and Dimensions

NEET 2016 · Physics · Units and Dimensions

Planck's constant ( h ) , speed of light in a vacuum ( c ) and...

Planck's constant (h)( h ), speed of light in a vacuum (c)( c ) and Newton's gravitational constant (G)( G ) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Options

  1. AhGc32\dfrac{\sqrt{hG}}{{c}^{\dfrac{3}{2}}}
  2. BhGc52\dfrac{\sqrt{hG}}{{c}^{\dfrac{5}{2}}}
  3. ChcG\sqrt{\dfrac{hc}{G}}
  4. DcGh32\sqrt{\dfrac{{cG }_{}}{h \dfrac{3}{2}}}

Correct answer

A. hGc32\dfrac{\sqrt{hG}}{{c}^{\dfrac{3}{2}}}

Step-by-step solution

L∝hacbGcL ∝ {h}^{a}{c}^{b}{G}^{c}

[L]{\left[L\right]}^{1} = {\left[{M}^{1}{L}^{2}{T}^{- 1}\right]}^{a}{\left[L{T}^{- 1}\right]}^{b}{\left[{M}^{- 1}{L}^{3}{T}^{- 2}\right]}^{c}

Solving,

a=12,c=12,b=−32a = \dfrac{1}{2}, c = \dfrac{1}{2}, b = - \dfrac{3}{2}

⇒L=hGc32⇒ L = \dfrac{\sqrt{hG}}{{c}^{\dfrac{3}{2}}}
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