The gravitational force between two object is F. It masses of both object are halved without changing distance between them, then the gravitation force would become

Options

A. F/4
B. F/2
C. F
D. 2F

Answer

A

Explanation

We know that, according to force of gravitation
`F=(gm_(1)m_(2))/(r^(2))(G="Gravitational constant")`
Where `m_(1) and m_(2)` are the masses of two objects respectively. And r is the distance between the two masses
Now, according to the question, if masses of both objects are halved,
i.e., `" "m_(1)^(')=(m_(1))/(2) and m_(2)^(')=(m_(2))/(2)`
New force `" "F^(')=(Gm_(1)^(')m_(2)^('))/(r^(2))=(G(m_(1))/(2)(m_(2))/(2))/(r^(2))`
`" "=(1)/(4)(Gm_(1)m_(2))/(r^(2))=(F)/(4) "where" (Gm_(1)m_(2))/(r^(2))=F`
So, new force `" "F^(')=(F)/(4)`
Thus, the new gravitational force will become `(1)/(4)` times of its original gravitational forcs.