Question

The force of attraction between two objects of masses 2m amd m is F₁.When the object with mass 2m is replaced with another object of mass m/2 ,the new force of attraction is found to be F₂.The ratio of F₁:F₂ IS:- (A)3:2 (B)2:3 (C)1:4 (D)=4:1 ⇒SPAMMER ARE REQUESTED TO STAY AWAY ⇒Need detailed answer from physics newton and other best user :)​

Answer 1

Force of attraction:

$\implies \bf F = \dfrac{Gm_1m_2}{r^2}$

where G = universal gravitational constant, m= masses, r = distance between the masses.

Solution:

Case 1

$\to\rm F_1 = \dfrac{ G\times 2m\times m}{r^2}$

$\to\rm F_1 = 2\bigg ( \dfrac{ Gm^2}{r^2}\bigg )$ ▪︎▪︎(1)

Case 2

$\to\rm F_2 = \dfrac{ G\times m\times m}{2r^2}$

$\to\rm F_2 = \dfrac{1}{2}\bigg ( \dfrac{ Gm^2}{r^2}\bigg )$

$\to\rm F_2 = \dfrac{1}{2}\bigg ( \dfrac{ F_1}{2}\bigg )$ ▪︎▪︎ (from 1)

$\to\rm \dfrac{F_2}{F_1} = \dfrac{1}{4}$

$\to\bf \dfrac{F_1}{F_2} = \dfrac{4}{1}$

★★ Ratio of F1 : F2 is 4 : 1

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