Question

Two spherical objects have masses of 3.1 x 10^5 kg and 6.5 x 10^3 kg. The gravitational attraction between them is 65 N. How far apart are their centers? (answer to 2 digits)

Answer 1

Answer:

4.55 x 10⁹m

Explanation:

Given parameters:

Mass of object 1  = 3.1 x 10⁵kg

Mass of object 2 = 6.5 x 10³kg

Gravitational force  = 65N

Unknown:

Distance between them  = ?

Solution:

To solve this problem, we use the expression below from the universal gravitational law;

    Fg  =    $\frac{G mass 1 x mass 2}{distance ^{2} }$  

   G = 6.67 x 10⁻¹¹

        65  = $\frac{6.67 x 10^{11} x 3.1 x 10^{5} x 6.5 x 10^{3} }{distance^{2} }$    

   Distance  = 4.55 x 10⁹m

         

Answer 2

Their centers are at the distance of "$4.55\times 10^9 \ m$".

Given:

Mass,

• $M_1 = 3.1\times 10^5 \ kg$
• $M_2 = 6.5\times 10^3 \ kg$

Gravitational force,

• $Fg = 65\ N$

We know,

• $G = 6.67\times 10^{-11}$

By using the Gravitational law, we get

→ $Fg= \frac{GM_1 M_2}{distance^2}$

By substituting the values, we get

→ $65 = \frac{6.67\times 10^{11}\times 3.1\times 10^5\times 6.5\times 10^3}{d^2}$

→   $d = 4.55\times 10^9 \ m$

Thus the response above is right.      

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