Physics, asked by conceptsofphysicshcv, 6 months ago

What will happen to gravitational force
between two objects if masses of both
objects are tripled?

Answers

Answered by Arighnach
26

Answer:

So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled.

Explanation:

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Answered by Mysterioushine
50

To Find :

  • Change in gravitational force when masses of both objects are tripled

Solution :

Gravitational force between two maases m₁ and m₂ when the distance of seperation between them is r is given by ,

 \\  \star \: {\boxed{\purple{\sf{F =  \dfrac{Gm_1m_2}{ {r}^{2} } }}}} \\  \\

Where ,

  • G is Gravitational constant

Let the original masses be m₁ and m₂ . Then the orginal gravitational force is ,

 \\  :  \implies \sf \:F_1  = \dfrac{Gm_1m_2}{ {r}^{2} }  \:  \: .........(1)\\  \\

Now , masses of objects when they are tripled is 3m₁ and 3m₂ and distance is r (since no change in distance is mentioned). Substituting the new masses ;

 \\  :  \implies \sf \:F_2=  \dfrac{G \times 3m_1 \times 3m_2}{ {r}^{2} }  \\  \\

 \\  : \implies \sf \: F_2 =  \dfrac{ 9Gm_1m_2}{ {r}^{2} }  \\  \\

 \\  :  \implies \sf \: F_2 = 9 \bigg( \dfrac{Gm_1m_2}{ {r}^{2} }  \bigg) \\  \\

 \\   : \implies{\underline{\boxed{\pink{\mathfrak{F_2 = 9F_1}}}}} \bigstar \\  \\

Hence ,

  • When the masses of objects are tripled keeping the distance between them constant the gravitational force becomes 9 times the original one.
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