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  4. The value of universal gravitational constant G=6.67 × 10-11 N m 2 kg -2 . The value of G in units of g -1 cm 3 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:

$G=6.67 \times 10^{-11} N m ^{2} kg ^{-2}$
$=6.67 \times 10^{-11} \times\left( kg m s ^{-2}\right) \times\left( m ^{2}\right) \times( kg )^{-2}$
$=6.67 \times 10^{-11} \times\left[(1000 g ) \times(100 cm ) \times s ^{-2}\right]$
$\times(100 cm )^{2} \times(1000 g )^{-2}$
$=6.67 \times 10^{-11} \times 10^{5} \times 10^{4} \times 10^{-6} g ^{-1} cm ^{3} s ^{-2}$
$=6.67 \times 10^{-8} g ^{-1} cm ^{3} s ^{-2}$