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The value of gravitation is G = 6.67 xx ...

The value of gravitation is `G = 6.67 xx 10^(-11)N-m^(2)/(kg^(2))` in SI units . Convert it into CGS system of units .

Text Solution

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The dimensional formula of G is `[M^(-1)L^(3)T^(-2)]`.
Using equation number (i), i.e.,
`n_(1)[M_(1)^(-1)L_(1)^(3)T_(1)^(-2)]=n_(2)[M_(2)^(-1)T_(2)^(-2)]`
`n_(2)=n_(1)[(M_(1))/(M_(2))]^(-1)[(L_(1))/(L_(2))]^(3)[(T_(1))/(T_(2))]^(-2)`
Here, `n_(1)=6.67xx10^(-11)`
`M_(1)=1kg," "M_(2)=1g=10^(-3)kg`
`M_(1)=1m," "L_(2)=1cm=10^(-2)m,`
`T_(1)=T_(2)=1s`
Substituting in the above equation, we get
`n_(2)=6.67xx10^(-11)[(1kg)/(10^(-3)kg)]^(-1)[(1m)/(10^(-2)m)]^(3)[(1s)/(1s)]^(2)`
or`" "n_(2)=6.67xx10^(-3)`
Thus, value of G in CGS system of units is
`6.67xx10^(-4)"dyne cm"^(2)//g^(2)`.
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