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

The energy (E), angular momentum (L) and universal gravitational const

1.	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
Answer» <html><body><p>zero<br/>`-1`<br/>`5//3`<br/>`1`<br/></p>Solution :(a) `hprop G^(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)<a href="https://interviewquestions.tuteehub.com/tag/l-535906" style="font-weight:bold;" target="_blank" title="Click to know more about L">L</a>^(y)E^(z)`<br/> <a href="https://interviewquestions.tuteehub.com/tag/write-746491" style="font-weight:bold;" target="_blank" title="Click to know more about WRITE">WRITE</a> the dimensions on both sides <br/> `[<a href="https://interviewquestions.tuteehub.com/tag/ml-548251" style="font-weight:bold;" target="_blank" title="Click to know more about ML">ML</a>^(2)T^(-1)]prop[M^(-1)L^(3)T^(-2)]^(x)[ML^(2)T^(-1)]^(y)[ML^(2)T^(-2)]^(z)` <br/> `[ML^(2)T^(-1)]=k[M^(-1)L^(3)T^(-2)]^(x)[ML^(2)T^(-1)]^(y)[ML^(2)T^(-2)]^(z)` <br/> Comparing the powers, we get <br/> `1=-x+y+z`...........(i) <br/> `2=3x+2y+2z` .........(ii) <br/> `-1=-2x=y-2z`...........(iii) <br/> On solving eqs (i), (ii) and (iii) we <a href="https://interviewquestions.tuteehub.com/tag/ger-468132" style="font-weight:bold;" target="_blank" title="Click to know more about GER">GER</a> <br/> `x=0`</body></html>