Question

What happens to the force between two objects, if

(i) the mass of one object is doubled ?
(ii) the distance between the objects is doubles and tripled ?
(iii) the masses of both objects are doubled ?​

Answer 1

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What happens to the force between two objects, if

(i) the mass of one object is doubled ?

Ans (i) If the mass of one of the objects is doubled, then the force of gravity between them is doubled. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.

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

Ans (ii) If the distance between the two objects is tripled, then Thus, the gravitational force between the two objects becomes one-ninth. (iii) If the masses of both the objects are doubled, then Thus, the gravitational force between the two objects becomes 4 times.

(iii) the masses of both objects are doubled ?

Ans (iii) If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.

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Answer 2

Step-by-step explanation:

$\Large\underline{\underline{\sf{\purple{Required\ Answer:-}}}}$

✯ Suppose two objects of masses $\sf {m_1}$ and $\sf {m_2}$ are lying at a distance $\sf {r}$ from each other. The force of gravitation between two objects is given by,

$\sf \: \: \: \: \: \: \: \: {\underline{\boxed{\red{\sf{F\ =\ \dfrac{Gm_1 m_2}{r^2}}}}}}$

➷ The mass of one object is doubled, $\sf {i.e.,}$ mass $\sf {m'_1\ =\ 2m_1}$

$\sf \: \: \: \: \: \: \: \: {\blue{F_1\ =\ \dfrac{G(2m_1) m_2}{r^2}\ =\ 2\dfrac{Gm_1 m_2}{r^2}\ =\ \bf 2F}}$

∴ The gravitational force also doubles, $\sf {i.e.,}$ it becomes twice the original value.

➷ When the distance between the objects is doubled, $\sf {i.e.,\ r'\ =\ 2r;}$ the gravitational force,

$\sf \: \: \: \: \: \: \: \: {\blue{F_2\ =\ \dfrac{Gm_1 m_2}{(2r)^2}\ =\ \dfrac{Gm_1 m_2}{4r^2}\ =\ \bf \dfrac{1}{4}F}}$

∴ The gravitational force becomes one-fourth of the original value.

➷ When the distance between the objects is tripled, $\sf {i.e.,\ 3r;}$ the gravitational force is given by,

$\sf \: \: \: \: \: \: \: \: {\pink{F_3\ =\ \dfrac{Gm_1 m_2}{(3r)^2}\ =\ \dfrac{Gm_1 m_2}{9r^2}\ =\ \bf \dfrac{F}{9}}}$

∴ The gravitational force becomes $\sf {\dfrac{1}{9}th}$ of the original force.

➷ The masses of both objects are doubled, mass of the object, $\sf {m'_1\ =\ 2m_1}$

Mass of second object, $\sf {m'_2\ =\ 2m_2}$

The gravitational force is given by,

$\sf \: \: \: \: \: \: \: \: {\pink{F_4\ =\ \dfrac{G(2m_1) (2m_2)}{r^2}\ =\ \dfrac{4\ Gm_1 m_2}{r^2}\ =\ \bf 4F}}$

∴ The gravitational force becomes four times the original value.