# Masses connected via string

Both the bodies are falling in gravity and as indicated by the picture and each body has a different mass

QUESTION-1(Direct question)

From the picture if the two masses were previously connected via a string and were left to free fall, would they have the same acceleration, or different acceleration. Explain your answer.

QUESTION-2(More of a hypothetical question)

If there was no string, then the masses would have freefall all the way down.

Now if we introduce a string(*) in between them, as shown in picture, it is clear that the tension(T) will act along the direction of fall of mass M, and opposite to direction of fall of mass N.

And, hence over time, the two falling masses would come closer and closer to each other. So, my question is, will the same scenario take place, if a string was introduced between M and N. So, my question is, what is the mistake in my analysis for the case where there string between the two bodies?

*:String is ideal

• Hint take the two blocks to be a system and neglect all internal forces and calculate the acceleration of each mass then take each mass and calculate tension force Sep 10, 2020 at 16:37

The two masses will have the same acceleration.
There is a thought experiment(due to Gallileo, I guess) to show that objects of different masses fall with same acceleration. It goes as follows:
Suppose you have a heavier object and a lighter object. You tie them up (like u have done in the picture), so then if the lighter objects falls slowly(less accelaration) and heavier object falls with a greater acceleration, then the lighter object will pull the heavier object. So the system will have an acceleration between the lighter and heavier object's acceleration.
But now the total object that you made by tying up the two objects is even more massive, so it should have even higher acceleration, but this goes against what we found out earlier(that the net system would have an acceleration in between the two constituent objects). This is a contradiction!
Only resolution is if both have same acceleration , so the body made up by tying the two will have the same acceleration.

Coming to the 2nd question, the string requires to be taut to provide any tension, if the two masses have same accelration and they start with same speed, they are at rest with respect to each other(the distance between them doesn't change, they don't pull each other), so the string isn't taut and it isn't providing any tension.

• Thank you sir . Sep 10, 2020 at 20:10

When they fall, it need not be that the string is taut always, The string only becomes taut if both the bodies are to pull away from each other. In this free fall case that you have shown, the first case and second case are practically equivalent.

• Thank you sir.. Sep 10, 2020 at 20:11