1.

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

Answer» Correct Answer - `6.67xx10^(-8) dyne cm^2 g^(-2)`
The dimensinal formula of G is `[M^(-1)L^3 T^(-2)]`
To convert MKS system to CGS system, we write
`M_1 = 1kg, L_1 =1m, T_1 =1s,`
`n_1 = 6.67xx10^(-11)`
`M_2 =1g, L_2 = 1cm, T_2 =1s, n_2 =?`
`n_2 =n_1((M_1)/(ML_2))^(-1) ((L_1)/(L_2))^3((T_1)/(T_2))^(-2)`
`=6.67xx10^(11)((1kg)/(1g))^(1) ((1m)/(1cm))^3 ((1s)/(1s))^(-2)`
`=6.67xx10^(-11)xx(10^3)^(-1)xx(10^2)^3xx1`
`=6.67xx10^(-8) dyne cm^2g^(-2)`


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