Question

The gravitational force between two bodies is F. If the mass of each body is tripled and the
distance between them is halved, then the force between them will be

Answer 1

Answer:

Given :

Gravitational force between 2 bodies is F ,

New mass is tripled in each body , distance between them is halved.

To find:

New gravitational force

Concept:

As per Newton's Law of Gravitation , we can say that :

• Force is directly proportional to the product of the masses
• Force is inversely proportional to the square of distance of separation.

Calculation:

$\boxed{ \huge{ \red{ \bold{F = G\dfrac{m1 \times m2}{ {r}^{2} } }}}}$

New masses are 3(m1) and 3(m2)

New distance is r/2.

New gravitational force be F2 :

$F2 = G\dfrac{3(m1) \times 3(m2)}{ { (\frac{r}{2}) }^{2} }$

$= > F2 = 36 \times \bigg(G\dfrac{m1 \times m2}{ {r}^{2} } \bigg)$

$= >F2 = 36( F)$

So final answer :

$\boxed{ \blue{ \huge{ \bold{F2 = 36( F)}}}}$

Answer 2

$\huge \mathtt{ \fbox{Solution :)}}$

Given ,

• The gravitational force between two bodies is F

• The mass of each body is tripled i.e 3m and 3M and distance between them is halved i.e r/2

Since ,

The gravitational force between two object in the universe is

• Directly proportional to the product of their masses and
• Inversely proportional to the square of the distance between them

$\large \mathtt{ \fbox{F = G\frac{mM}{ {(r)}^{2} } }}$

Where , G = universal gravitation constant which is 6.67 × (10)^(-11) Nm²/kg²

By the given condition ,

$\sf \mapsto F_{new} = \frac{G \times 9mM }{ { (\frac{r}{2}) }^{2} } \\ \\\sf \mapsto F_{new} = \frac{G \times 9mM \times 4}{ {(r)}^{2} } \\ \\ \sf \mapsto F_{new} = \frac{36 \times G \times mM }{ {(r) }^{2} } \\ \\ \sf \mapsto F_{new} = 36F$

Hence , the new gravitational force is 36 times the gravitational force

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