The gravitational force between two bodies having masses ${\text{m}}_{\text{1}}{\text{,m}}_{\text{2}}$ respectively when they are separated by a distance R is equal to F now mass of first body is halved and mass of second body is doubled without changing the separation between them then force between them will be equal to

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.

New gravitational force can be found by:

${\text{F}}^{|}=\frac{{\text{Gm}}_1^{|}{\text{m}}_2^{|}}{{\text{R}}^{\text{2}}}$
${\text{m}}_1^{|}=\frac{{\text{m}}_{\text{1}}}{\text{2}},{\text{\hspace{0.17em}\hspace{0.17em}m}}_2^{|}={\text{2m}}_{\text{2}}$

${\text{F}}^{|}=\frac{\text{G}\frac{{\text{m}}_{\text{1}}}{\text{2}}\times {\text{2m}}_{\text{2}}}{{\text{R}}^{\text{2}}}=\frac{\text{G}{\text{.m}}_{\text{1}}{\text{m}}_{\text{2}}}{{\text{r}}^{\text{2}}}=\text{F}$

Therefore, option B is the correct answer.