Question

Two masses $m_1$ and $m_2$ are separated by a distance $d$. Find by how many times the force of gravity increases if mass of each of the objects is doubled without change in the distance between them.

Answer 1

Formula $F=\frac{G.m_1{m}_2}{d^2}$

Initial force $=\frac{G.m_1{m}_2}{d^2}$

Force after change in masses

Substitution:

$F^{\prime }=\frac{G.2m_1\times 2m_2}{d^2}$

$F^{\prime }=\frac{4G{m}_1{m}_2}{d^2}$

$\therefore F^{\prime }=4\left(\frac{G{m}_1{m}_2}{d^2}\right)$

$F^{\prime }=4\left(F\right)$.

Gravitational fore increases by $4$ times.