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  4. The value of universal gravitational constant G=6.67 × 10-11 N m2 kg-2. The value of G in units of g-1 cm3 s-2 is

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Q. The value of universal gravitational constant $G=6.67 \times 10^{-11}\,N\,m^{2}\,kg^{-2}$. The value of $G$ in units of $g^{-1}\, cm^3\, s^{-2}$ is

Physical World, Units and Measurements

Solution:

$G=6.67 \times 10^{-11}\,N\,m^{2}\,kg^{-2}$
$=6.67 \times 10^{-11} \times \left(kg\,ms^{-2}\right)\left(m^{2}\right)\left(kg\right)^{-2}$
$=6.67 \times 10^{-11} \times \left[\left(1000\,g\right)\times \left(100\,cm\right)\times s^{-2}\right] $ $\times \left(100\,cm\right)^{2} \times \left(1000\,g\right)^{-2}$
$=6.67 \times 10^{-8}\,g^{-1}\,cm^{3}\,s^{-2} $