Question

A body of mass $50kg$ and another body of mass $60kg$ are separated by a distance of $2m$. What is the force of attraction between them?

Answer 1

Obtain the mathematical expression for the force of attraction between two bodies from Newton’s universal law of gravitation. Then substitute the given values of masses of bodies and distance between them. Using simple mathematics, compute the force.

Complete step by step answer:
The universal law of gravitation gives us the mathematical expression of the force of attraction between two objects of mass m and M separated by a distance R as,
$F = \dfrac{{GmM}}{{{R^2}}}$ and $G = {\text{gravitational constant}} = 6.67 \times {10^{ - 11}}Nk{g^{ - 2}}{m^2}$
Where, G is the universal gravitational constant. Let the mass of the two bodies are m and M. Again, let the initial separation between the two bodies are r. Given, the force of attraction between the two bodies is to be found ?. So, we can write that,
$F = \dfrac{{GmM}}{{{R^2}}} = ?$
Now, the separation between the two bodies is given in question as $2m$.
$\Rightarrow R = 2m$
And masses of bodies are given as $m = 50kg$ and $M = 60kg$
Now we take all these values in the given formula
$F = \dfrac{{GmM}}{{{R^2}}}$
$\Rightarrow F = \dfrac{{6.67 \times {{10}^{ - 11}} \times 50 \times 60}}{{{2^2}}} = 5.025 \times {10^{ - 8}}N$
Therefore, the force of attraction between the two bodies when the separation between them is $2m$ will be $5.025 \times {10^{ - 8}}N$.

Note:
The force of attraction between two bodies is directly proportional to the product of the mass of the two bodies and inversely proportional to the square of the separation between the two bodies. As the separation between the body decreases, the force of attraction between the two bodies will increase and as the separation between the two bodies increases, the force of attraction between the two bodies will decrease.