Question

Gravitational force between two object of mass 10kg and 15kg is 8×10^-8 N. Then find out separation between objects.

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Answer 1

Given :

• Masses of the objects (m₁ and m₂) = 10 kg and 15 kg

• Gravitational force of attraction (G) = 8 × 10⁻⁸ N

To Find :

• The distance of seperation between the objects

Solution :

The Expression for gravitational force of attraction between two masses is given by,

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

$\\ \\ \sf{where}\begin{cases}& \sf{G\:is\:Gravitational\:constant}\\ &\sf{m_1 \:is\:the\:mass\:of\:first\:object}\\ &\sf{m_2\:is\:the\:mass\:of\:another\:object} \\& \sf{r \: is \: distance \: of \: seperation \: between \: the \: masses} \end{cases}$

Substituting the values in the formula ,

$\\ : \implies \sf \: 8 \times {10}^{ - 8} \: = \dfrac{(6.67 \times {10}^{ - 11}) (10 \: )(15 \: )}{ {r}^{2} }$

$\\ : \implies \sf \: 8 \times {10}^{ - 8} = \frac{150\times 6.67 \times {10}^{ - 11} }{ {r}^{2} }$

$\\ : \implies \sf \: 8 \times {10}^{ - 8} \times {r}^{2} = 1000.5 \times {10}^{ - 11}$

$\\ : \implies \sf \: {r}^{2} = \dfrac{1000.5 \times {10}^{ - 11} }{8 \times {10}^{ - 8} }$

$\\ : \implies \sf \: {r}^{2} = 125 \times {10}^{ - 3}$

$\\ : \implies \sf \: r \: = \sqrt{125 \times {10}^{ - 3} }$

$\\ : \implies{\underline{\boxed{\pink{\sf{ \: r = 0.35 \: m}}}}} \: \bigstar$

Hence ,

• The distance of seperation between them is 0.35 m

Note :

G = 6.67 × 10⁻¹¹ Nm²/kg²

Answer 2

Answer:

0.35 m

Explanation:

Given:

• Gravitational force (F) between two objects = 8 × $\sf{10^-8}$
• $\sf{Mass\:(m_1)}$ = 10 kg
• $\sf{Mass\:of\:another\:object\:(m_2)\:=\:15 \:kg}$

To find:

• Distance/separation between two objects (d) = ?

Solution:

By universal law of gravitaion, we comes to know that if there are any two bodies of mass "M" and "m" are kept at a distance "d" attracts each other with a force of attraction which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

In this case the Gravitational force (F) = $\sf{\dfrac{GMm}{d^2}}$

Here, G is known as universal gravitational constant. Value of G = 6.67 × $\sf{10^-11}$ Nm²/kg².

(Substitute all the given values)

$\implies\:\sf{8\:×\:10^-⁸\:=\:6.67\:×\:10^-11\:\dfrac{10\:×\:15}{d^2}}$

$\:$

$\implies\:\sf{8×10^-⁸\:=\:\dfrac{66.7\:×\:15\:×\:10^-¹¹}{d^2}}$

$\:$

$\implies\:\sf{8\:×\:10^-⁸\:×d^2\:=\:1000.5\:×\:10^-¹¹}$

$\:$

$\implies\:\sf{d^2\:=\:\dfrac{1000.5\:×\:10^-¹¹}{8\:×\:10^-⁸}}$

$\:$

$\implies\:\sf{d^2\:=\:125\:×\:10^-³}$

$\:$

$\implies\:\sf{d\:=\:\sqrt{125\:×\:10^-³}}$

$\:$

$\implies\:\sf{d\:=\:0.35\:m}$

$\:$

Hence, separation between the objects is 0.35 meters.