Question

If the distance between two masses is increased by a factor of 5by what factor would the mass of one of them have to attract to maintain the same gravitational force?would this be an increase or decrease in the mass

Answer 1

$F\ \alpha\ \frac{M}{R^2}$

If R' = 5R
F' = F
M' = ? M

$\frac{F'}{F} = \frac{M'}{R'^2} \div \frac{M}{R^2}\\ \\ \Rightarrow \frac{F'}{F} = \frac{M'}{R'^2} \times \frac{R^2}{M}\\ \\ \Rightarrow \frac{F'}{F} = \frac{M'}{M} \times \frac{R^2}{R'^2}\\ \\ \Rightarrow 1 = \frac{M'}{M} \times \frac{1}{25} \\ \\ \Rightarrow \frac{M'}{M} = 25 \times 1 \\ \\ \Rightarrow M' = 25M$

The mass should be increased to 25 times the initial mass