If speed of light (c), acceleration due to gravity (g) and pressure (P) are taken as fundamental units, the dimensions of gravitational constant (G) are

If speed of light (c), acceleration due to gravity (g) and pressure (P

1.	If speed of light (c), acceleration due to gravity (g) and pressure (P) are taken as fundamental units, the dimensions of gravitational constant (G) are
Answer» <html><body><p>`[c^(0)gP^(-3)]`<br/>`[c^(2)g^(3)P^(-2)]`<br/>`c^(0)g^(2)P^(-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)]`<br/>`c^(2)g^(2)P^(-2)]`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Let`G= kc^(x)g^(y)P^(z)` <br/>Where k is a dimensionless constant. <br/> `:. [M^(-1)L^(3)T^(-2)]= [LT^(-1)]^(x)[LT^(-2)]^(y)[ML^(-1)T^(-2)]^(z)= [M^(z)L^(x+y-z)T^(-x-2y-2z)]` <br/> Applying <a href="https://interviewquestions.tuteehub.com/tag/principle-1166255" style="font-weight:bold;" target="_blank" title="Click to know more about PRINCIPLE">PRINCIPLE</a> of <a href="https://interviewquestions.tuteehub.com/tag/homogeneity-1028735" style="font-weight:bold;" target="_blank" title="Click to know more about HOMOGENEITY">HOMOGENEITY</a> of dimensions we get, <br/> z=- 1...(i) <br/> x+y-z= 3...(ii) <br/>-x-2y-2z= -2,..(iii) <br/> On solving (i), (ii) and (iii) we get, <br/> `x=0, y=2, z=-1 :. [G]= [c^(0)g^(2)P^(-1)]`</body></html>