Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

Options

A. `(1)/(4)` times
B. 4 times
C. `(1)/(2)` times
D. unchanged

Answer

B

Explanation

We know that, according to gravitational force
`F=G(Mm)/(r^(2))`
where, F = Force between Two moss
M = First moss
m = Second mass
G = Gravitational Constart
r = Distant between Two mass
According to the question,
`F^(')` = New force when mass is doubled
If mass of each particle is doubled
i.g., M=2M and m=2m
These value put in Eq. (i), we get
`F^(')=G((2M)(2m))/(r^(2))`
`F^(')=4G(Mm)/(r)`
From Eq. (i), `F^(')=4F`