What happens to the gravitational force between two objects if the mass of one object is halved?

To do:

To find the force between two objects, if

$(i)$. the mass of one object is doubled?

$(ii)$. the distance between the objects is doubled and tripled?

$(iii)$. the masses of both objects are doubled?

Solution:

We know the formula for gravitational force between two objects:

$\boxed{F=G\frac{mM}{d^2}}$

Where,

$F\rightarrow$gravitational force

$G\rightarrow$gravitational constant

$M\rightarrow$mass of object 1

$m\rightarrow$mass of the object 2

$d\rightarrow$distance between object 1 and object 2

$(i)$. When the mass of one object is doubled:

Then, the mass of object 1 becomes $2M$

Then, the gravitational force between object 1 and object 2

 $F'=G\frac{m(2M)}{d^2}$

Or $F'=2(G\frac{mM}{d^2})$

Or $F'=2F$

Therefore, if the mass of one object is doubled, then the force is also doubled.

$(ii)$ When the distance between the objects is doubled and tripled:

If the distance between the objects is doubled

Then distance becomes $2d$

Then gravitational force $F'=\frac{(GmM)}{(2d)^2}$

Or $F'=\frac{1}{4}(\frac{GmM}{d^2})$

Or $F'=\frac{F}{4}$

Therefore, gravitational force becomes one-fourth of its initial force when the distance between two objects is doubled.

Now, if it’s tripled

$F'=\frac{(GmM}{(3d)^2}$

$F'=\frac{1}{9}(G\frac{mM}{d^2})$

Or $F'=\frac{F}{9}$

Therefore, gravitational force becomes one-ninth of its initial force when the distance between two objects is tripled.

$(iii)$. When the masses of both objects are doubled:

If the masses of both the objects are doubled, then

$F'=G\frac{(2m)(2M)}{d^2}$

$F'=4F$ 

Therefore, gravitational force will become four times greater than its actual value.

The gravitational force between two objects is F. If both of their masses are halved without altering the distance between them, the new gravitational force between them would be:A. F/4B. 2 FC. F /2D. 4 F

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∴Fnew=F4.

it becomes 4 times as great as it was originally (Notice that 'distance between them' means the distance between their centers of mass. So, for example, in order to double the distance between you and the Earth, you'd have to rise about 4,000 miles off of the surface.)