Question

The gravitational force between two objects is 6N. Find the new gravitational force between the objects when :

(i) if the distance between the two objects is doubled

(ii) If the distance between the two objects are halved

(iii) if the mass of one of the objects is doubled

Answer 1

Answer:

answers in the attachment

Answer 2

Answer -

i) $\implies$$\bf F' = \dfrac{3}{2} F$

ii)$\implies$ $\bf F' = 24N$

iii) $\implies$$\bf F' = 12N$

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Solution -

Given -

Gravitation force between two object is 6N.

To find -

Gravitational force when

i) distance is doubled.

ii) distance is halved.

iii) mass of one object is doubled.

Formula used -

$\boxed{\bf \purple{F = \dfrac{Gm_1 m_2}{{r}^{2}}}}$

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Gravitational force when distance is doubled -

$\bf F = \dfrac{Gm_1 m_2}{{r}^{2}}$

$\implies$$\bf F' = \dfrac{Gm_1 m_2}{{2r}^{2}}$

$\implies$$\bf F' = \dfrac{Gm_1 m_2}{4{r}^{2}}$

$\implies$$\bf F' = \frac{1}{4} F$

$\implies$$\bf F' = \frac{6}{4} N$

$\implies$$\bf\purple{ F' = \dfrac{3}{2} N}$

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Gravitational force when distance is halved -

$\bf F = \dfrac{Gm_1 m_2}{{r}^{2}}$

$\implies$$\bf F' = \dfrac{Gm_1 m_2}{{ \frac{r}{2}}^{2}}$

$\implies$$\bf F' = \dfrac{Gm_1 m_2}{{ \frac{r^2}{4}}}$

$\implies$$\bf F' = \dfrac{4Gm_1 m_2}{r^2}$

$\implies$$\bf F' = 4F$

$\implies$$\bf F' = 4 \times 6N$

$\implies$$\bf\purple{ F' = 24 N}$

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Gravitational force when mass of one object is doubled -

$\bf F = \dfrac{Gm_1 m_2}{{r}^{2}}$

$\implies$$\bf F' = \dfrac{G(2m_1) m_2}{{r}^{2}}$

$\implies$$\bf F' = \dfrac{2Gm_1 m_2}{{r}^{2}}$

$\implies$$\bf F' = 2F$

$\implies$$\bf F' = 2 \times 6N$

$\implies$$\bf \purple{F' = 12 N}$

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