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Question

A tube 1 cm2 in cross section is attached to the top of a vessel 1 cm high and of cross section 100 cm2. Water is poured into the system filling it upto a height of 100 cm above the bottom of the vessel as shown in the figure. Take g=10 m/s2. Find the correct statement. Take atmospheric pressure P0=105 bar.


A
The force exerted by the water against the bottom of the vessel is 1100 N.
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B
The weight of water in the system is 1.99 N.
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C
Both (a) and (b) are correct.
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D
Neither (a) nor (b) is correct.
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Solution

The correct option is C Both (a) and (b) are correct.
Force exeted by the water against the bottom of the vesel Fbase=Pbase× Area of base
Pbase=P0+ρwgh
=105+103×10×[(99+1)100]
[h=(99+1) cm=1 m]
=1.1×105 N/m2

Area of base=100×104 m2 [given]
Fbase=1.1×105×102=1100 N


Weight of the water in the system
=Weight of water in tube of cross-sectional area 1 cm2 + Weight of water in vessel of cross-sectional area 100 cm2
i.e Wsystem=Wtube+Wvessel
=ρgV1+ρgV2
=103×10×[V1+V2]
=104×[99×1+1×100]×106
=1.99 N

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