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Question

A cylindrical vessel of cross-sectional area 1000cm2, is fitted with a frictionless piston of mass 10kg, and filled with water completely. A small hole of cross-sectional area 10mm2 is opened at a point 50cm deep from the lower surface of the piston. The velocity of efflux from the hole will be

A
10.5m/s
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B
3.4m/s
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C
0.8m/s
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D
0.2m/s
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Solution

The correct option is A 3.4m/s
Given that
A=1000cm3
m=10kg=10000g
Ah=10mm2=0.1m2
(Hh)=50cm
Here, the force on piston is
F=mg

Hence, Increase in pressure on the liquid in the wider tube is
P=FA=mgA
Let, H is the level of water to which piston will move, thus
P=Hρg
H=Pρg
H=mgAρg=mAρ
H=100001000.......(ρ=1)
H=10cm from surface of tube.

Since, (Hh)=50cm,H=60cm=0.6m
The velocity of effluent from the hole is
v=hρg
v=(2gh)
v=(2)(9.8)(0.6)=3.4ms1

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