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  • Confused! kindly explain, Planck's constant (h), speed of light in vacuum (c) and Newton's gravitationalconstant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

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

  • Option 1)

    \frac{{\sqrt {hg} }}{{c^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}

  • Option 2)

    \frac{{\sqrt {hg} }}{{c^{{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} }}

  • Option 3)

    \sqrt {\frac{{hc}}{g}}

  • Option 4)

    \sqrt {\frac{{Gc}}{{h^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}}

 

Answers (1)

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Option 1)

\frac{{\sqrt {hg} }}{{c^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}

Option 2)

\frac{{\sqrt {hg} }}{{c^{{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} }}

Option 3)

\sqrt {\frac{{hc}}{g}}

Option 4)

\sqrt {\frac{{Gc}}{{h^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} }}}

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Aadil

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