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Friday, 5 August 2011

Physics GRE - #4

Consider an hourglass on a scale pictured below at times t=0, 0.001, and 1 hour. What happens to the scale's measure of weight of the hourglass plus the sand combination as the sand falls?

  • The weight is constant
  • The weight decreases and then increases
  • The weight increases
  • The weight increases and then decreases

    Solution :

    Initially the hourglass has all its sand on the bottom and so its at a weight W.

    When we invert the hourglass, the weight decreases as the falling sand do not contribute their weight to the weight of the hourglass (so at 0.001 s, the weight of the hourglass is less than W).

    When the sand hits the bottom of the hourglass, the momentary impulse delivered by the sand makes the hourglass weigh heavier than it actually is, so at exactly one hour, the hourglass is heavier than W. Thus the weight of the hourglass decreases and then increases.


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