<p>When two solid spheres of the same material and same radius <em>r</em> are in

Question

<p>When two solid spheres of the same material and same radius <em>r</em> are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to<br /><br />a. <em>r</em><br />b. <em>r</em>²<br />c. <em>r</em>³<br /><strong>d. <em>r</em>⁴</strong><br />e. <em>r</em>⁶</p>
<p>&#160;</p>
<p><strong>(d) </strong>is the expected answer. However please show how and why it is.</p>

Explanation / Answer

gravitational force   Fg = G(m)(m)/r2 where both have same material so density is same and distance is 2r    then      Fg = G ( 4/3 * r3 ) ( 4/3 * r3 )/ ( 2r)2            =   G( 4/3 *) ( 4/3 * ) r6/ 4r2            = G ( 4/9)2 r4    where G ( 4/9)2 is constant so Fg is directly propotional to r4    where G ( 4/9)2 is constant so Fg is directly propotional to r4

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