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Kisachek [45]
2 years ago
14

orange{ Question}}" alt=" \large\frak{ \orange{ Question}}" align="absmiddle" class="latex-formula">
The force of attraction (A) between two objects, whose masses are fixed, varies inversely with the square of their distance of separation (d). The force of attraction between them is 2 units when the dis- tance is 5 cm. What is the distance between the two objects, if the attraction between them is 8 units?
\pink \dag \:   \pink{\large\rm{ No \:  spam}}
\red \dag  \: \red{\large\rm{ With \:  explanation }}
​
Mathematics
1 answer:
SVEN [57.7K]2 years ago
7 0

Answer:

\boxed{\sf distance \: between \:  the \: objects \: \: is  \: 2.5 \: cm}

Step-by-step explanation:

According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to

the product of their masses, given by standard formula.

A = G \cdot  \frac{m_1.m_2}{ {d}^{2} }

where A,d & G are force of attraction, distance of separation & proportionality constant respectively.

<em>Given:</em>

A1 = 2 units

d1= 5 cm

A2 = 8 units

<em>To find:</em>

Distance of separation when the force of attraction is 8 units d2 = ?

<em>Solution:</em>

Substituting the given values in above at each point,

A_1 = G \cdot  \frac{m_1.m_2}{ {d_1}^{2} }  \\ 2 = G \cdot  \frac{m_1.m_2}{ {5}^{2} }  \\  \sf similarly  \: at \:  second \:  point \:  of  \: attraction \\  A_2 = G \cdot  \frac{m_1.m_2}{ {d_2}^{2} }  \\ 8 = G \cdot  \frac{m_1.m_2}{ {d_2}^{2} }  \\  \sf \: \: dividing \:  both  \: of \:  the \:  equation \\  \frac{2}{8}  =  \frac{G \cdot  \frac{m_1.m_2}{ {5}^{2} }}{G \cdot  \frac{m_1.m_2}{ {d_2}^{2} } }  \\  \sf \: G \: m_1 and \: m_2  \: are \:   \: constant  \: hence  \\ \sf  they \:  can  \: be  \: cancelled \:  out  \\  \frac{2}{8}  =  \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } }  \\  \sf rearranging \: above \: equation \\  \frac{1}{4}  =  \frac{{d_2}^{2} }{ {5}^{2} }  \\ {d_2}^{2}  =   \frac{ {5}^{2} }{4 }  \\ {d_2}^{2}  =  \frac{25}{4}   \\ {d_2}^{2}  = 6.25 \\  \sqrt{{d_2}^{2} }  =  \sqrt{6.25}  \\  \boxed{ \sf{d_2} = 2.5 \: cm}

<em>Answer:</em><em> </em><em>the distance between the two </em><em>objects </em><em>is </em><em>2</em><em>.</em><em>5</em><em> </em><em>cm</em><em>, if the attraction between them is 8 </em><em>units.</em>

<em><u>Learn more about universal law of gravitation here brainly.com/question/27244479</u></em>

<em>Thanks </em><em>for </em><em>joining </em><em>brainly </em><em>community</em><em>!</em>

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