Answer to Question #128742 in Physics for Quadri

Question

2 identical spheres are place at a distance so that force of attraction between them is s if 50% of mass of 1 sphere is transferred to other sphere then what will be the change of force of attraction

Answer 1

Let's denote masses of each sphere as $m$. At the initial distance $r$ the force of attraction is $F_1$. According to the Newton's gravity law, this force will be:

$$F_1 = G\dfrac{m\cdot m}{r^2} = G\dfrac{m^2}{r^2}$$

After the redistribution of masses, the first sphere will have the mass $m/2$ and the second one - $3m/2$. Then the attraction force will be:

$$F_2 = G\dfrac{\frac{m}{2}\cdot \frac{3m}{2}}{r^2} = \dfrac{3}{4}G\dfrac{m^2}{r^2}$$

Dividing the second force by the first, obtain:

$$\dfrac{F_2}{F_1} = \dfrac34$$

Thus, the force of attraction becomes 3/4 times less, then the initial one.

Answer. 3/4 times less.