Question

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

• A. Zero
• B. 33.5 $\times$ ${10}^{-11}$ N
• C. 46.69 $\times$ ${10}^{-11}$ N
• D. 13.19 $\times$ ${10}^{-11}$ N

Answer 1

The correct option is D 13.19 $\times$ ${10}^{-11}$ N

As gravitational force is an attractive force, the $5kg$ and $7kg$ masses attract the $4kg$ mass in opposite directions.
So, the net force is the subtraction of the two forces acting on the $4kg$ mass.

The gravitation force due to $5kg$ on $4kg$ is:
$F_1=\frac{GmM}{d^2}$ $=\frac{6.67\times {10}^{-11}\times 4\times 5}{2^2}$
$=33.5\times {10}^{-11}N$ (The direction of force is towards 5 kg mass).

The gravitational force due to $7kg$ on $4kg$:
$F_2=\frac{GmM}{d^2}$ $=\frac{6.67\times {10}^{-11}\times 4\times 7}{2^2}$
= 46.69 $\times$ ${10}^{-11}$ N (The direction of force is towards 7 kg mass).
Since, the force on 4 kg masses due to $5kg$ mass is opposite to the force due to $7kg$ on $4kg$ mass. The net force is the subtraction of both the forces.
Net force on $2kg$ mass = $(46.69-33.5)\times$ ${10}^{-11}N$ = $13.19\times$ ${10}^{-11}N$.