72. Problem 17.28 (RHK) The tension in a string holding a solid block below the
surface of a liquid (of density greater than the solid) is
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Solution: Click For PDF Version Let the area of cross-section of the solid block be A
and its height be h. Its volume V will be Ah. Let the
density of the solid block be
It is immersed in a liquid of density
We will draw free-body diagram of the block in two situations: one when the container is at rest and two when the container is under upward acceleration a. Situation (i) Let
Situation (ii)
In this situation the container, the liquid, and the block are under upward acceleration a. As the liquid is under acceleration, the gauge pressure in it will vary with
depth h as
As the string remains stretched when the block is under upward acceleration, tension T in it can be found by applying the Newton’s second law of motion on the accelerated motion of the block. The equation of motion of the block in this situation is
In the above expression by substituting
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