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Physics Question on Units and measurement

The value of universal gravitational constant G=6.67×10−11 N m2 kg−2G=6.67 \times 10^{-11}\,N\,m^{2}\,kg^{-2}. The value of GG in units of g−1 cm3 s−2g^{-1}\, cm^3\, s^{-2} is

A

6.67×10−86.67 \times 10^{-8}

B

6.67×10−76.67 \times 10^{-7}

C

6.67×10−96.67 \times 10^{-9}

D

6.67×10−106.67 \times 10^{-10}

Answer

6.67×10−86.67 \times 10^{-8}

Explanation

Solution

G=6.67×10−11 N m2 kg−2G=6.67 \times 10^{-11}\,N\,m^{2}\,kg^{-2} =6.67×10−11×(kg ms−2)(m2)(kg)−2=6.67 \times 10^{-11} \times \left(kg\,ms^{-2}\right)\left(m^{2}\right)\left(kg\right)^{-2} =6.67×10−11×[(1000 g)×(100 cm)×s−2]=6.67 \times 10^{-11} \times \left[\left(1000\,g\right)\times \left(100\,cm\right)\times s^{-2}\right] ×(100 cm)2×(1000 g)−2\times \left(100\,cm\right)^{2} \times \left(1000\,g\right)^{-2} =6.67×10−8 g−1 cm3 s−2=6.67 \times 10^{-8}\,g^{-1}\,cm^{3}\,s^{-2}