Question

Three masses $5kg$, $4kg$ and $7kg$ are aligned in a straight line as shown below. Find the net gravitational force on $4kg$?

• A. $46.69\times {10}^{-11}N$
• B. $13.34\times {10}^{-11}N$
• C. $0$
• D. $33.5\times {10}^{-11}N$

Answer 1

The correct option is B $13.34\times {10}^{-11}N$

Gravitational force is an attractive force, and the directions of force for the $5kg$ and $7kg$ mass are shown in the diagram shown.

Using the universal law of gravitation for $4kg$ and $5kg$ mass, we get:
$F_1=\frac{Gm{M}_A}{d_A^2}$

Similarly,
$F_2=\frac{Gm{M}_B}{d_B^2}$

Clearly, the two forces are acting in opposite direction. So, net force will be the difference of the two forces.):
$F=F_2-F_1$
$F=\frac{Gm{M}_B}{d_B^2}-\frac{Gm{M}_A}{d_A^2}$
$F=Gm(\frac{M_B}{d_B^2}-\frac{M_A}{d_A^2})$
Subsituting values, we get:
$F=6.67\times {10}^{-11}\times 4\times (\frac{7}{2^2}-\frac{5}{2^2})$
$F=13.34\times {10}^{-11}N$