Two objects of masses 4 kg and 3 kg are placed along x and y - axis respectively at a distance of 1 m from the origin. An object of mass 1 kg is kept at the origin of the co-ordinate system. Then the resultant gravitational force of attraction on the object at the origin is

Given:

Two objects ${\text{m}}_1=4\text{kg}$ kept on x axis at a distance 1 m from origin, ${\text{m}}_2=3\text{kg}$ kept on y – axis at a distance 1 m from origin

Another mass 1 kg is kept at origin.
 

Gravitational force is the force of attraction between any two objects having some mass. It is given by:
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$

Where M and m are the masses of the objects, r is the distance between them and G is the universal gravitational constant having the value of 6.67 X 10^-11 Nm²/kg².

$\text{F}=\sqrt{{\text{F}}_1^2+{\text{F}}_{\text{2}}^{\text{2}}}$

${\text{F}}_{\text{1}}=\frac{{\text{Gm}}_{\text{1}}{\text{m}}_{\text{3}}}{{\text{r}}^{\text{2}}}=\frac{G\left(4\right)\left(1\right)}{{\left(1\right)}^2}$         

${\text{F}}_{\text{1}}=\text{4 G}$

${\text{F}}_{\text{2}}=\frac{{\text{Gm}}_{\text{1}}{\text{m}}_{\text{2}}}{{\text{r}}^{\text{2}}}=\frac{G\left(1\right)\left(3\right)}{{\left(1\right)}^2}$

${\text{F}}_{\text{2}} =\text{3G}$

$\text{F}=\sqrt{{\left(3\text{G}\right)}^2+{\left(4\text{G}\right)}^2}$               

$\text{F}=\sqrt{25{\text{G}}^2}=5\text{G}$

$\text{F}=\text{5}\times \text{6}.\text{67}\times \text{1}{0}^{-\text{11}}$

$\text{F}=\text{3}.\text{335}\times \text{1}{0}^{-\text{1}0} \text{N}$