Question

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

Spammers Get lost
Don't answer if you don't know

​

Answer 1

Explanation:

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,

$\begin{gathered} \\ \star \: {\boxed{\purple{\sf{F = \dfrac{Gm_1m_2}{ {r}^{2} }}}}} \\ \end{gathered} </p><p>⋆ </p><p>F= </p><p>r </p><p>2</p><p> </p><p>Gm </p><p>1</p><p> </p><p> m </p><p>2$

$\begin{gathered} \\ \\ \sf{where}\begin{cases}& \sf{G\:is\:Gravitational\:constant}\\ &\sf{m_1 \:is\:the\:mass\:of\:first\:object}\\ &\sf{m_2\:is\:the\:mass\:of\:another\:object} \\& \sf{r \: is \: distance \: of \: seperation \: between \: the \: masses} \end{cases}\\ \\\end{gathered} </p><p>where </p><p>⎩</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎨</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎪</p><p>⎧</p><p> </p><p> </p><p> </p><p> </p><p>GisGravitationalconstant</p><p>m </p><p>1</p><p> </p><p> isthemassoffirstobject</p><p>m </p><p>2</p><p> </p><p> isthemassofanotherobject</p><p>risdistanceofseperationbetweenthemasses</p><p> </p><p> </p><p> </p><p> </p><p>$

Substituting the values in the formula ,

$\begin{gathered} \\ : \implies \sf \: 8 \times {10}^{ - 8} \: = \dfrac{(6.67 \times {10}^{ - 11}) (10 \: )(15 \: )}{ {r}^{2} } \\ \\ \end{gathered} </p><p>:⟹8×10 </p><p>−8</p><p> = </p><p>r </p><p>2</p><p> </p><p>(6.67×10 </p><p>−11</p><p> )(10)(15)$

$\begin{gathered} \\ : \implies \sf \: 8 \times {10}^{ - 8} = \frac{150\times 6.67 \times {10}^{ - 11} }{ {r}^{2} } \\ \\ \end{gathered} </p><p>:⟹8×10 </p><p>−8</p><p> = </p><p>r </p><p>2</p><p> </p><p>150×6.67×10 </p><p>−11</p><p>$

$\begin{gathered} \\ : \implies \sf \: 8 \times {10}^{ - 8} \times {r}^{2} = 1000.5 \times {10}^{ - 11} \\ \\ \end{gathered} </p><p>:⟹8×10 </p><p>−8</p><p> ×r </p><p>2</p><p> =1000.5×10 </p><p>−11$

$</p><p>\begin{gathered} \\ : \implies \sf \: {r}^{2} = \dfrac{1000.5 \times {10}^{ - 11} }{8 \times {10}^{ - 8} } \\ \\ \end{gathered} </p><p>:⟹r </p><p>2</p><p> = </p><p>8×10 </p><p>−8</p><p> </p><p>1000.5×10 </p><p>−11$

$\begin{gathered} \\ : \implies \sf \: {r}^{2} = 125 \times {10}^{ - 3} \\ \\ \end{gathered} </p><p>:⟹r </p><p>2</p><p> =125×10 </p><p>−3$

$\begin{gathered} \\ : \implies \sf \: r \: = \sqrt{125 \times {10}^{ - 3} } \\ \\ \end{gathered} </p><p>:⟹r= </p><p>125×10 </p><p>−3$

$\begin{gathered} \\ : \implies{\underline{\boxed{\pink{\sf{ \: r = 0.35 \: m}}}}} \: \bigstar \\ \\ \end{gathered} </p><p>:⟹ </p><p>r=0.35m</p><p>$

★

Hence ,

The distance of seperation between them is 0.35 m

Note :

$G = 6.67 × 10⁻¹¹ Nm²/kg²$

Answer 2

Answer:

pls don't hurt your fingers ✌️