Will a Large Body on Earth's Surface Pull a Smaller Body Towards Itself?

[mkbh_10]

We know that N = mg , where N is normal reaction and mg is the force with which Earth is pulling a body . Now if i place another body ,lets say 10 ^12 kgs at a distance of 1 m from the body , will the larger body pull the smaller body horizontally towards itself , both these bodies are in contact with the surface of Earth , not joined to surface. will friction come into play in opposing the attraction towards each other ??

Now the problem i am facing is that when the larger body rests on the surface, it automatically becomes part of (earth+body) which is a composite system and 10^12 < < 10^24(mass of Earth ) so the smaller body won't experience any pull unless the mass becomes comparable to the order of Earth's mass and if we have a very dense body , 10^12 kg packed in a meter then it will pull the smaller body with a force of 6.7 m/s^2 which is comparable to 9.8 of Earth .

Also it must be that for the larger body to pull smaller one it shud have mass much greater than Earth to overcome Earth's gravity

 

[banerjeerupak]

As soon as you put another large mass into the system, you have to consider the shifting of the centre of mass. The Earth will exert a pull on this body and this body will exert a force of attraction on the earth. The centre of mass will shift according to the mass of this new body in space and the mass of the earth. so the small mass will shift towards the common centre of mass.

 

[sir-pinski]

and pull the smaller one towards it.

Firstly, it is important to clarify that the equation N = mg is only applicable in situations where the object is at rest on a flat surface. In this scenario, the normal reaction force (N) is equal and opposite to the force of gravity (mg) acting on the object.

In the given scenario, if we place another body of 10^12 kg at a distance of 1 m from the first body, there will be a gravitational force of attraction between the two bodies. This force will be given by the equation F = GmM/r^2, where G is the universal gravitational constant, m and M are the masses of the two bodies, and r is the distance between them.

However, since both bodies are in contact with the surface of Earth and not joined to it, the normal reaction force will also come into play. This force will act in the opposite direction to the gravitational force between the two bodies.

As for the question of friction, it will depend on the coefficient of friction between the two bodies and the surface they are in contact with. If the coefficient of friction is high enough, it can oppose the gravitational force and prevent the two bodies from moving towards each other.

Moreover, as you have mentioned, for the larger body to pull the smaller body towards it, it would need to have a mass much greater than Earth's mass. This is because Earth's gravity is much stronger compared to the gravitational force between two relatively smaller objects.

Overall, the scenario described raises interesting questions about the role of gravity and normal reaction forces in a composite system. It also highlights the importance of considering all the relevant forces and factors when analyzing a physical problem.