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An hourglass is being weighed on a sensitive balance, first when sand is dropping in a steady stream from the upper to the lower part, and then again after the upper part is empty. Are the two weights the same or not? Explain your answer.

An hourglass is being weighed on a sensitive balance, first when sand is dropping in a steady stream from the upper to the lower part, and then again after the upper part is empty. Are the two weights the same or not? Explain your answer.

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
No, the weight will not be the same.
In the first case the weight will be more because when the sand from the upper half falls at the bottom it provides momentum to the pan on which the hourglass rests. This momentum will increase the net force on the arm of the balance, and the beam will move towards the position of the hourglass. Therefore one will have to add more mass on the other side of the beam to balance the hourglass thereby accounting for its large weight.
In the second case the sand is accumulated at the bottom and no momentum is imparted to the pan carrying the hourglass. This reduces the net force from the pan relative to the first case and the beam would balance against smaller mass, thereby accounting for less weight of the hourglass.
Rizwan Mahsood
41 Points
4 years ago
No the weights are not same.As we know that a moving body has momentum and a body at rest not, thus in the first case the sands are in motion and must have some momentum that will exert force when strike`s the bottom, (F=P/dt) as force is proportional to momentum. In this case the mass will greater.In the other case the sands are at rest having zero momentum thus it will not exert any force on the bottom (F=0 because P=0).So in this case the mass will be less.

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