Question

If the distance between two masses be doubled, then the force between will become
$\left( a \right){\text{ 1/4 times}}$
$\left( b \right){\text{ 4 times}}$
$\left( c \right){\text{ 1/2 times}}$
$\left( d \right){\text{ 2 times}}$

Answer 1

Hint According to Newton's law of motion of gravitation each object or body within the universe attracts and each object towards one another which force of attraction is directly proportional to the merchandise of their plenty and reciprocally proportional to the sq. of the gap between them. By keeping this in mind we can answer this.
Formula used:
Force,
$F = \dfrac{{GMm}}{{{R^2}}}$
Here,
$F$, will be the force

Complete Step By Step Solution The power of gravity between the two articles will diminish as the separation between them increments. The two most significant elements influencing the gravitational power between two items are their mass and the separation between their focuses. As mass increases, so does the power of gravity, however, an expansion in separation mirrors an opposite proportionality, which makes that power decline dramatically.
So, as we know by the newton’s law of gravitation;
$F = \dfrac{{GMm}}{{{R^2}}}$
So according to the question,
If $R$ is doubled then the new resulting force will be given by
$\Rightarrow {F_{new}} = \dfrac{{GMm}}{{{{\left( {2R} \right)}^2}}}$
On solving it we get
$\Rightarrow {F_{new}} = \dfrac{{GMm}}{{4{R^2}}}$
Therefore, the ratio of the two forces will be
$\Rightarrow \dfrac{{{F_{new}}}}{F} = \dfrac{4}{1}$
Hence from this, we can say that
$\Rightarrow \dfrac{F}{4} = New{\text{ }}force$
So we can say that there will be a quarter of the gravitational force.

Hence the option $A$ will be correct.

Note : If you are considering only gravitational force, then the force would reduce by a factor of four. This adheres to Newton's Law of Gravitation: Force of fascination between any two bodies is straightforwardly corresponding to the result of their masses and is conversely relative to the square of their separations.