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The speed of light c, acceleration due t...

The speed of light `c`, acceleration due to gravity `g` and pressure `p` are taken as fundamental units, the dimensions of gravitational constant `G` are :

A

`c^(0)gp^(-3)`

B

`c^(2)g^(3)p^(-2)`

C

`c^(0)g^(2)p^(-1)`

D

`c^(2)g^(2)p^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `G=c^(x)g^(y)p^(z)`
`M^(-1)L^(3)T^(-2)=[L^(1)T^(-1)]^(x)[L^(1)T^(-2)]^(y)[ML^(-1)T^(-2)]^(z)`
`=M^(z)L^(x+y-z)T^(-x-2y-2z)`
Then`z=-1,x+y+1=3,-x-2(y+z)=-z`
or`-x-2y+2=-2`
`-(x+y)-y=-4`
`-2-y=-4` or `y=2`
`x=0`
`:.G=c^(0)g^(2)p^(-1)`
Hence correct choice is `(c )`.
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