If the speed of light ( c ) , acceleration due to gravity ( g ) and pressure ( p ) are taken as the fundamental quantities, then the dimension of gravitational constant is

Question

If the speed of light ( c ) , acceleration due to gravity ( g ) and pressure ( p ) are taken as the fundamental quantities, then the dimension of gravitational constant is, c 2 g 0 p − 2, c 0 g 2 p − 1, c g 3 p − 2, c − 1 g 0 p − 1

MARKS App · Accepted Answer

Let [ G ] ∝ c x g y p z by substituting the following dimensions : [ G ] = [ M − 1 L 3 T − 2 ] , [ c ] = [ LT − 1 ] , [ g ] = [ LT − 2 ] [ p ] = [ ML − 1 T − 2 ] and by comparing the powers of both sides we can get x = 0 , y = 2 , z = − 1 ∴ [ G ] ∝ c 0 g 2 p − 1

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