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Q.

Suppose the gravitational force between two objects placed at a distance r is F. Is it true that if the distance between them doubles, the force will also be doubled?

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a

True

b

False

answer is B.

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Detailed Solution

The above statement is false.
The gravitational force between two objects is given by
F1 =

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

                       G = gravitational constant
r = distance between two objects
m1 = mass of the object 1
m2 = mass of object 2
                                  If the distance between the objects is doubled, then the gravitational force becomes one-fourth since,

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

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

Dividing F1 by F2

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

\Rightarrow F_{1} = 4 F_{2}

\Rightarrow F_{2} = \frac{F_{1}}{4}

The correct statement would be, If the distance between the objects is doubled, then the gravitational force becomes one-fourth.

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