Question

$\star \; {\underline{\boxed{\red{\pmb{\frak{ \; Question \; :- }}}}}}$

$\longmapsto$ What happens to the force between two objects in following Conditions :-

$\rightarrowtail$ The Mass of One Object is doubled .

$\rightarrowtail$ The Distance between the objects is doubled .

$\rightarrowtail$ The Distance between the objects is Tripled .

$\rightarrowtail$ The Masses of both Objects are Doubled .

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$\red{❒ }$ Good Luck ...!!​

Answer 1

$\large{\underline{\underline{\bigstar\; \sf{AnswEr\;:}}}}$

Here, we are asked to calculate the force between two objects at 3 different conditions. In order to solve this question, we firstly need to know the formula gravitational force between the two objects. We know,

$\qquad\qquad\star\; \underline{\boxed{\mathcal{F=G\dfrac{Mm}{{d}^{2}}}}}$

where:

• F represents the force in Newtons.
• M represents the mass of object 1.
• m represents the mass of object 2.
• d represents the distance between the two objects.
• G represents the Gravitational constant.

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( I ) The mass of one object is doubled.

• Let the mass of object 1 (M) be doubled. So,

$\longrightarrow\quad\sf{Mass\; of\; {object}_{1}=2M}$

Equating this value in the formula, we get:

$\longrightarrow\quad\sf{{F}_{1}=G\times\dfrac{2M\times m}{{d}^{2}}}$

Multiplying G with the fraction.

$\longrightarrow\quad\sf{{F}_{1}=\dfrac{G\times 2M\times m}{{d}^{2}}}$

Now,

$\longrightarrow\quad\sf{{F}_{1}=\dfrac{2GMm}{{d}^{2}}}$

We know, GMm/d² is equal to F. So,

$\longrightarrow\quad\sf{{F}_{1}=2F}$

$\qquad\leadsto\quad$ Henceforth, if the mass of one object is doubled the force gets doubled.

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( II ) The distance between the objects is doubled.

• Let the distance between the objects be doubled, so:

$\longrightarrow\quad\sf{Distance\; between\; two\; objects=2d}$

Equating this value in formula, we get:

$\longrightarrow\quad\sf{{F}_{2}} = \dfrac{2GMm}{{2d}^{2}}$

Now,

$\longrightarrow\quad\sf{{F}_{2}=\dfrac{GMm}{4{d}^{2}}}$

We know, GMm/d² equals to F. Therefore,

$\longrightarrow\quad\sf{{F}_{2}=\dfrac{F}{4}}$

$\qquad\leadsto\quad$ Henceforth, if the distance between the objects is doubled the force gets 1/4.

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( III ) The distance between the objects is tripled.

• Let the distance between the objects is tripled, so:

$\longrightarrow\quad\sf{Distance\; between\; two\; objects=3d}$

Equating the value in formula, we get:

$\longrightarrow\quad\sf{{F}_{3}=\dfrac{GMm}{{3d}}^{2}}$

Now,

$\longrightarrow\quad\sf{{F}_{3}=\dfrac{GMm}{9{d}^{2}}}$

We know, GMm/d² equals to F, so:

$\longrightarrow\quad\sf{{F}_{3}=\dfrac{F}{9}}$

$\qquad\leadsto\quad$ Henceforth, if the distance between the objects is tripled so the force gets 1/9.

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( IV ) The masses of both objects are doubled.

• Let the mass of object 1 be 2M and the mass of object 2 be 2m. So,

$\longrightarrow\quad\sf{{F}_{4}=\dfrac{G\times 2M\times 2m}{{d}^{2}}}$

Now,

$\longrightarrow\quad\sf{{F}_{4}=\dfrac{4GMm}{{d}^{2}}}$

We know, GMm/d² equals to F. So,

$\longrightarrow\quad\sf{{F}_{4}=4F}$

$\qquad\leadsto\quad$ Henceforth, if the masses of both objects are doubled so the force gets quadrupled.

Answer 2

Answer:

As per the universal law of gravitation, every object in the universe attracts every other object by the force of attraction which is directly proportional to the product of masses of the objects and is inversely proportional to the square of the distance between them. This is mathematically given as:

F = G(mM/d2)

Where,

F is the force of the gravitational pull

G is the constant known as the gravitational constant

M is the mass of object 1

m is the mass of the object 2

d is the distance between object 1 and object 2

(i) The mass of one object is doubled?

According to the universal law of gravitation, the force between 2 objects (m1 and m2) is proportional to their plenty and reciprocally proportional to the sq. of the distance(R) between them.

F = G(2mM/d2)

If the mass is doubled for one object.

F = 2F, so the force is also doubled.

(ii) The distance between the objects is doubled and tripled

If the distance between the objects is doubled and tripled

If it’s doubled

Hence,

F = (GmM)/(2d)2

F = 1/4 (GmM)/d2

F = F/4

Force thus becomes one-fourth of its initial force.

Now, if it’s tripled

Hence,

F = (GmM)/(3d)2

F = 1/9 (GmM)/d2

F = F/9

Force thus becomes one-ninth of its initial force.

(iii) The masses of both objects are doubled?

If masses of both the objects are doubled, then

F = G(2mM/d2)

F = 4F, Force will therefore be four times greater than its actual value.

Explanation:

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