Laws of Gravitation may be redefined?
Classical Mechanics
Level
3
Consider two bodies in space experiencing only mutual gravitational forces of each other. Now that the both form a system together, you may consider the following assumptions.
- Only mutual gravitational forces acting on each other.
- Both have same mass but different volumes.
- No revolution or rotation but only translation motion towards each other.
- And finally, the mass of the bigger body has been concentrated on the left side of its center.
Where does the center of gravity of the system lie?
Exactly in the middle of the line joining the centers of the two bodies
None of them
Towards the bigger body
Towards the denser body
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1 solution
Scenario A: Imagine two identical bodies of same mass (m1 = m2 = 400 units) and volume (v1 = v2 = 400 units) separated at a distance of 100 units. If the system is considered to lie on X axis with one body being at origin and the other at 100 units on the X+ side, then we can say that the center of mass (often called "CG") of the system lies at 50 units from the origin because everything is same between the bodies except for their positions.
where m1 & m2 being the masses of the bodies and R1 & R2 their positions on the axis.
Scenario B: Now, imagining that one of the two bodies has been given more volume but keeping the same mass, we may say that the density of the body being disturbed which also means that some amount of its mass moving away from the other body whose parameters have not changed, there occurs some disturbance in the CG of the system too. Here is why; Consider the same bodies and values as before but this time cut a mass of 100 units from the one that lies at the origin and place that piece at -100 units. i.e. on the X- side. Now using the same formula, we may calculate the CG of the entire system now considering the three bodies and their parameters; m1 = 300 units, v1 = 300 units and R1 = 0 units m2 = 400 units, v2 = 400 units and R2 = 100 units m3 = 100 units, v3 = 100 units and R3 = -100 units
We get the value of CG in this scenario as ~ 37.5 units . So comparing the CGs of the Scenario A and Scenario B , the position of the CG is moved towards the bigger body because of the density disturbance.