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Consider a ball tied to a string and it is imparted a velocity we have studied that condition for looping the loop is that tension at the uppermost point must be zero, but why is this condition imposed please explain?

If tension becomes zero at some point below the uppermost point won't the ball complete the loop because it still has some velocity?

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If the tension is equal zero at some point below the uppermost level, the tension at higher points would need to be negative for the circular motion to continue. Of course, the tension cannot be negative, instead, the rope would become loose and the object would fall.

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  • $\begingroup$ thank you very much sir for replying,but what about the trajectory of particle after reaching the topmost point?no condition is need for that? what if the ball drops after reaching the topmost point? $\endgroup$ – Ajay Sabarish Mar 7 '16 at 2:57
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An object that is not acted upon (with tension) will follow a parabolic curve. So instead of a circle, the object will track a parabola for the duration of the time where tension is zero.

It is the tension that forces an object to follow a prescribed path.

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  • $\begingroup$ thank you very much sir for replying,but what about the trajectory of particle after reaching the topmost point?no condition is need for that? what if the ball drops after reaching the topmost point? $\endgroup$ – Ajay Sabarish Mar 7 '16 at 2:57
  • $\begingroup$ @AjaySabarish the answer to that is to compute the tension as a function of angle. You'll find that the minimum is when the particle is at the top of the curve: so if it is $\ge 0$ there, it is $\ge 0$ everywhere. $\endgroup$ – tfb Mar 7 '16 at 13:22
  • $\begingroup$ No because the parabola it would follow if at he top the tension is zero and stays zero would be bigger than the circle. You would need tension to make it curve around a circle. $\endgroup$ – John Alexiou Mar 7 '16 at 13:28
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At highest point the body has minimum tension but the velocity of the body is greater compared to some point of the curve hence a body continued in its circular path.

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