as per gravtiational law, it is said that the force of attraction is indirectly proportional to the square of the distance between the two centres of the body attraction.
lets take a big circular ring and place a ball inbetween it. In this case if the ball is at the centre then it means that distance between their two centres are zero, which essentially means the force is infinite and the ball cannot be taken out of the ring.
The above statement makes the law incorrect!!!
Does it mean the newton was incorrect from the moment he proposed it ???
Answer1:
no i think newton proposed its law for discrete infinitesimally small chunks of matter.
this law holds for spherical large bodies as well because, they have a field similar to a point mass but this is not the case for a circular ring. its field can be obtained by integration and not concentrating the entire mass to the COM.
this law holds for spherical large bodies as well because, they have a field similar to a point mass but this is not the case for a circular ring. its field can be obtained by integration and not concentrating the entire mass to the COM.
Answer2:
Integration would yield the correct result
COM can only be used when the field has to be calculated away from the mass, not inside it!
COM can only be used when the field has to be calculated away from the mass, not inside it!
and by the way, integration would probably yield that the net force on the ball is zero
Answer3:
yeah!
newton believed that gravitation acted instantaneously which is not possible.
newton believed that gravitation acted instantaneously which is not possible.
Answer4:
Well, we have to consider every particle of the ring and not its COM. COM comes to play only when we consider the both as a system and calculate the net external force on the system.
But what you got is not a flaw, I guess. Yes. it says that the gravitational force exerted on the ball is infinite while having a common COM. But even a very small disturbance(any other external force) can cause the ball to move out of its position and no longer it is displaced out the ring's COM, it becomes easy to move the ball.
I think this too is wrong.
But what you got is not a flaw, I guess. Yes. it says that the gravitational force exerted on the ball is infinite while having a common COM. But even a very small disturbance(any other external force) can cause the ball to move out of its position and no longer it is displaced out the ring's COM, it becomes easy to move the ball.
I think this too is wrong.
Answer5:
lets take a big circular ring and place a ball inbetween it. In this case if the ball is at the centre then it means that distance between their two centres are zero, which essentially means the force is infinite and the ball cannot be taken out of the ring.
The force is ZERO. See: http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell
The force is ZERO. See: http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell
Answer6:
Only for an external mass, you can assume the mass to be at the centre of mass.
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