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If the value of universal gravitational ...

If the value of universal gravitational constant is `6.67xx10^(11) Nm^2 kg^(-2),` then find its value in CGS system.

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We know, `F= G(m_(1)m_(2))/(r^2)`
where F = gravitational force
`m_(1),m_(2)` = mass of two bodies exerting gravitational force on each other
r = distance between the bodies
`G=(Fr^2)/(m_(1)m_(2))`
`implies [G] ([MLT^(-2)][L^2])/([M^2])=[M^(-1)L^(3)T^(-2)]`
Comparing with `[M^(a)L^(b)T^(c )]`, we have a= -1, b= 3 and c= -2
`n_(2)= n_(1)[(M_1)/(M_2)]^(a)[(L_1)/(L_2)]^(b)[(T_1)/(T_2)]^(c )`
`=6.6xx10^(-11)[10^(3)]^(-1)[10^2]^(3)[1]^(-2)`
`=6.6xx10^(-11)xx10^(-3)xx10^(6)`
`=6.6xx10^(-8)" dyne "cm^(2)g^(-2)`.
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