Question

8. Two spheres of mass 2 kg and 3 kg respectively are situated so that the gravi- tational force between them is 2,5 x 10-8 N. Calculate the distance between them.​

Answer 1

Question :-

• Two spheres of mass 2 kg and 3 kg respectively are situated so that the gravitational force between them is $\bf 2.5 \times 10^{-8 }N$Calculate the distance between them.

We are given :-

• Mass of first sphere, m = 2 kg
• Mass of second sphere, M= 3 kg
• Gravitational force ,F = $\bf 2.5 \times 10^{-8} N$
• G = 6.67×10⁻¹¹ Nm²/kg²

We are asked to find distance between them.

• We know that according to gravitational law, we have force of attraction between two bodies is directly proportional to the product of masses of bodies and inversely proportional to the square of distance between them.Which is given by –

$\qquad$ $\pink{\twoheadrightarrow\sf F = \dfrac{GmM}{r^2}}$

Substituting values, we get –

$\qquad$ $\twoheadrightarrow\sf 2.5\times 10^{-8} = \dfrac{6.67\times10^{-11}\times2\times3}{r^2}$

$\qquad$ $\twoheadrightarrow\sf 2.5\times 10^{-8} = \dfrac{4.002\times10^{-8}}{r^2}$

$\qquad$ $\twoheadrightarrow\sf \dfrac {r^2}{4.002\times10^{-10}}=\dfrac{1}{2.5\times10^{-8}}$

$\qquad$ $\twoheadrightarrow\sf r^2 = \dfrac{4.002\times10^{-10}}{2.5\times10^{-8}}$

$\qquad$ $\twoheadrightarrow\sf r^2 = 1.6 \times 10^{-10}\times 10^{8}$

$\qquad$ $\twoheadrightarrow\sf r^2 = 1.6 \times 10^{-10+8}$

$\qquad$ $\twoheadrightarrow\sf r^2= 1.6\times10^{-2}$

$\qquad$ $\twoheadrightarrow\sf r=\sqrt{1.6\times10^{-2}}$

$\qquad$ $\twoheadrightarrow\sf r=1.265\times10^{-1} \: m$

$\qquad$ $\pink{\twoheadrightarrow\bf r = 12.65 \:cm}$

• Henceforth,distance between them will be 12.65 cm.