Question

the gravitational force btw 2 objects is 2N .calculate the gravitational force btw them if the distance btw them is doubled​

Answer 1

Answer:

$\boxed{\bold{\mathfrak{F' = 0.5 \ N}}}$

Given:

Gravitational force between 2 objects (F) = 2 N

To Find:

Gravitational force between 2 objects if the distance between them is doubled (F')

Explanation:

Gravitational force of attraction between two particles:

$\boxed{ \bold{F = \frac{Gm_1 m_2}{r^2} }}$

As force is to be calculated between same object:

$\therefore$

$\bold{ F \propto \frac{1}{r^2}} \: \: \: \: \: \: ...eq_1$

So, when distance between two objects is doubled gravitational force of attraction will be:

$\implies F ' \propto \frac{1}{{(2r)}^{2}} \\ \\ \implies \bold{F ' \propto \frac{1}{4{r}^{2}}} \: \: \: \: \: ...eq_2$

Dividing $eq_2$ by $eq_1$ we get:

$\implies \frac{F '}{F } = \frac{ \frac{1}{4 {r}^{2} } }{ \frac{1}{ {r}^{2} } } \\ \\ \implies \frac{F '}{F } = \frac{ \cancel{{r}^{2}} }{4 \cancel{{r}^{2} }} \\ \\ \implies \frac{F '}{F } = \frac{1}{4} \\ \\ \implies F '= \frac{F}{4} \\ \\ \sf Substituting \: value \: of \: F = 2 : \\ \\ \implies F ' = \frac{2}{4} \\ \\ \implies F ' = \frac{1}{2} \\ \\ \implies F ' = 0.5 \: N$

$\therefore$

Gravitational force between 2 objects if the distance between them is doubled (F') = 0.5 N

Answer 2

$\huge\bold{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• The gravitational force between two objects is “2N” .

TO FIND :-

• The gravitational force between the two objects, if the distance between them is doubled .

CALCULATION :-

$<font color=blue>$

Let,

✍️ The mass of two objects be $\underline\bold{m_1}$ and $\underline\bold{m_2}$ .

✍️ G be the Universal Gravitational Constant .

✍️ d be the distance between two objects .

Then, gravitational force of attraction between the two objects is

$\pink\bigstar\:\rm{\purple{\boxed{\red{Force(F)\:=\:G\:\dfrac{m_1\:m_2}{d^2}\:}}}}$

According to the question if distance between the two objects is doubled, then new distance between them is

• d' = 2d .

So, the new gravitational force of attraction between them is

$<font color=green>$

$\rm{\implies\:F_{new}\:=\:G\:\dfrac{m_1\:m_2}{d'^{2}}\:}$

$\rm{\implies\:F_{new}\:=\:G\:\dfrac{m_1\:m_2}{(2d)^2}\:}$

$\rm{\implies\:F_{new}\:=\:G\:\dfrac{m_1\:m_2}{4\:d^2}\:}$

$\rm{\implies\:F_{new}\:=\:\dfrac{1}{4}\:\left\{\:G\:\dfrac{m_1\:m_2}{d^2}\:\right\}\:}$

$\rm{\red{\implies\:F_{new}\:=\:\dfrac{F}{4}\:}}$

✍️ Putting the value of “F = 2N” in the above equation,

$\rm{\implies\:F_{new}\:=\:\dfrac{2}{4}\:}$

$\rm{\boxed{\red{\implies\:F_{new}\:=\:0.5\:N\:}}}$

$\pink\therefore$ $<font color=gray>$ The gravitational force of attraction between the two objects is “0.5 N”, when the distance between them is doubled .