Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out. (a) What will be the answers to the problem ? (b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.
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(a) In this case the atmospheric pressure on the surface of the water = zero.
Hence, the pressure of water at the bottom of the glass =ρgh
=1000*10*(20/100) N/m²
=2000 N/m²
Hence the force by the water on the bottom
=2000 N/m²*(20/10000) m²
=4 N Downwards.
(b) Whatever be the shape of the glass the resultant horizontal force by the glass on the water will be zero and the resultant verical force by the glass on the water = weight of the water = 0.50*10 N = 5 N.
Hence the force by the side of the glass on the water
= 5 N -1000*10* (20/100)*(20/10000) N
= 5 N - 4 N
= 1 N upward.
As we see that the force by the bottom of the glass on the water depends on the height of water and the bottom area, also the total vertical force by the glass on the water depends only on the volume of the water. These do not depend on the shape of the glass. Thus the force by the glass side on the water will remain the same if the height, the bottom area and the volume are unchanged.
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