Calculate the dimensions of universal gravitational constant G. What is the value of G in `SI` units if its value in CGS system is `6.67xx10^(-8)` units?

Answer

`[M^(-1) L^(3) T^(-2)]; 6.67xx10^(-11) SI` units

Explanation

Its dimensional formula is `[M^(-1)L^(3)T^(-2)]`
`G=6.67xx10^(-8) cm^(3)//gs^(2)`
`1 cm=10^(-2) m` and `1g=10^(-3) kg`
So, `G=6.67xx10^(-8) ((10^(-2) m)^(3))/((10^(-3)kg)(s^(2)))`
`=6.67xx10^(11) m^(3)/(kg s^(2))`