Physics

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant (h) is

Zero

SOLUTION
$h={ G }^{ x }{ L }^{ y }{ E }^{ z }$
$\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -1 } \right]= { \left[ { M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 } \right] }^{ x }{ \left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -1 } \right] }^{ y }{ \left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 } \right] }^{ z }$

Comparing the power, we get
$1=-x+y+z$               ...(i)
$2=3x+2y+2z$          ...(ii)
$-1=-2x-y-2z$           ...(iii)
On solving equations (i), (ii) and (iii), we get
$x=0$

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Single Correct Medium Published on 18th 08, 2020
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