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If the value of $G$, the gravitational constant in C. G. S. system is $6.70 \times 10^{-8}$, then what is its value in S. I. unit?

Ans. If the value of $G$, the gravitational constant in C. G. S. system is $6.70 \times 10^{-8}$, then its value in S.I. unit will be $6.70 \times 10^{-11}$

The dimension of $G$ is $\left[M^{-1} L^{3} T^{-2}\right]$

we have, $N _{1} U _{1}= N _{2} U _{2}$

$\therefore \quad N _{1} = N _{2}\left[\frac{ U _{2}}{ U _{1}}\right]$

$= N _{2}\left[\frac{ M _{2}}{ M _{1}}\right]^{-1}\left[\frac{ L _{2}}{ L _{1}}\right]^{3}\left[\frac{ T _{2}}{ T _{1}}\right]^{-2}$

$= N _{2}\left[\frac{10^{-3} kg }{1 kg }\right]^{-1}\left[\frac{10^{-2} \text { metre }}{1 \text { metre }}\right]^{3}\left[\frac{ sec }{ sec }\right]^{-2}$

$=6.70 \times 10^{-8} \times 10^{-3}=6.70 \times 10^{-11}$

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