Question

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

Answer 1

Correct Answer - `(6.67 xx 10^(-8) cm^(3)//g s^(2))`
Dimension of gravitational constant = `[ M^(-1)L^(3) T^(-2)]`
`" "n_2= n_1[(M_1)/(M_2)]^(-1) [(L_1)/(L_2)]^(3) [ (T_1)/(T_2)]^(-2)`
here
`" "{:(MKS,,CGS),(n_1 = 6.67 xx 10^(-11),,n_2= ?), (M_1 = kg,,M_2 = g), (L_1 = m,,L_2 = cm), (T_1= sec,, T_2 = sec):}`
`n_2 = 6.67 xx 10^(-11) [ (kg)/(g)]^(-1) [(m)/(cm)]^(3) [(sec)/(sec)]^(2) `
` = 6.67 xx 10^(-11) xx 10^(-3) xx 10^(6) xx 1`
` = 6. 67 xx 10 ^(-8)`