Question

If the gravitational force between objects of equal mass is 2.3 * 10 raised to - 8 N, when the objects are 10 m apart, what is the mass of each object?plz give correct answer ​

Answer 1

$\large \underline \bold{Given :-}$

$\small \bold{Gravitational \: Force \: (Fg) = 2.3\times 10^{-8} \: N}$

$\small \bold{distance \: between \: objects \: (r) = 10 \: m}$

$\small \bold{masses \: of \: each \: object = m1 = m2 = m}$

$\large \underline \bold{To Find :-}$

$\small \bold{Calculate \: the \: mass \: of \: each \: object = \: ?}$

$\large \underline \bold{Gravitational \: Force :-}$

$\: \: \: \: \:$$\small \bold{Fg =\dfrac{Gm1m2}{r^{2}}}$

$\small \bold{Where \: , \: G = 6.67\times 10^{-11} \: \dfrac{Nm^{2}}{Kg^{2}}}$

$\large \underline \bold{Solution :-}$

$\small \bold{On \: Using \: the \: above \: formula -}$

$\small \bold{Fg =\dfrac{Gm^{2}}{r^{2}}}$

$\small \bold{m^{2} =\dfrac{Fg \: r^{2}}{G}}$

$\small \bold{m^{2} =\dfrac{2.3\times 10^{-8}\times 10^{2}}{6.67\times 10^{-11}}}$

$\small \bold{m^{2} =\dfrac{2.3\times 10^{-6}}{6.67\times 10^{-11}}}$

$\small \bold{m^{2} =\dfrac{2.3\times 10^{5}}{6.67}}$

$\small \bold{m^{2} =\dfrac{23\times 10^{4}}{6.67}}$

$\small \bold{m^{2} = 3.45\times 10^{4}}$

$\small \bold{m = 1.86\times 10^{2} \: Kg}$

$\small \bold{m = 186 \: Kg}$

$\small \bold{mass \: of \: each \: object \: is \: 186 \: Kg .}$