Question

Give the S.I. unit of G and its value.

Answer 1

Step 1: Formula used

The acceleration due to gravity in terms of the gravitational constant is,

$g=\frac{GM}{r^2}$ [ where $g=$the acceleration due to gravity, $G=$gravitational constant, $M=$the mass of earth, $r=$radius of the earth ]

Step 2: S.I. Unit of each component

SI unit of $g=m/s^2,M=kg,r=m$

Step 3: SI Unit of $G$

Putting the S.I. unit of each component in the above gravitational constant formula

$$\begin{gathered} G=\frac{g\times r^2}{M} \\ G=\frac{(m/s^2){\left(m\right)}^2}{kg} \\ Multiplyingdenominatorandnumeratorbykg \\ G==\frac{\left(kg\right)(m/s^2)\left(m^2\right)}{k{g}^2} \\ G=\frac{N{m}^2}{k{g}^2}[As1N=kgm/s^2] \\ G=N{m}^{2}k{g}^{-2} \end{gathered}$$

Step 4: Value of $G$

Initially, the value of $G$ was proposed by Newton.

$ValueofG=6.67408\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Thus, the S.I. unit of $G$ (universal gravitational constant) is $=N{m}^{2}k{g}^{-2}$ and the value of $G$ (universal gravitational constant) is $=6.67408\times {10}^{-11}N{m}^{2}k{g}^{-2}$.