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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



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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
1 4 1
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