Is it true that if the mass of two and the distance between them are doubled, then the gravitational force between them in Newton will change to $\frac{F}{16}$ ?

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True

False

answer is B.

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Detailed Solution

The above statement is False.
According to the universal law of gravitation, “the force between any two objects or bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them”. Mathematically,

F α \frac{m_{1} m_{2}}{r^{2}}

Or,

F = G \frac{m_{1} m_{2}}{r^{2}}

Where,

F

is the gravitational force between two bodies,

m_{1}

and

m_{2}

are masses of the first and the second body respectively and

r

is the separation between the two objects.
As,

r ’ = 2 r

, then

\Rightarrow

F ’ = G \frac{m_{1} m_{2}}{r^{2}}

\Rightarrow = G \frac{m_{1} m_{2}}{{(2 r)}^{2}}

\Rightarrow = G \frac{m_{1} m_{2}}{4 r^{2}}

Therefore, the force of attraction will change to

\frac{F}{4}

.
The correct statement would be that if the mass of two and distance between them are doubled, then the gravitational force between then in Newton will change to