Question

Determine the value and units of universal Gravitational constant, G.

Answer 1

We know, gravitational acceleration due to earth is given by,

$g=\frac{GM}{R^2}$...........(i)

where G = Universal gravitational constant

M = Mass of the earth = $5.97\times {10}^{24}$ Kg.

R = Radius of the earth = 6378.1 Km.

Now we have,

g = 9.8$\frac{m}{s^2}$..............(ii)

Equating equations (i) and (ii) and putting the values we get,

9.8 = $\frac{G\times 5.97\times {10}^{24}}{{(6378.1\times 1000)}^2}$

G =$6.67\times {10}^{-11}$ N$\frac{m^2}{k{g}^2}$.

Thus SI units of G are N$\frac{m^2}{k{g}^2}$.