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Question

A large tank is filled with water (density=103 kg/m3). A small hole is made at a depth of 10 m below water surface. The range of water coming out of the hole is R on the ground. What extra pressure must be applied on the water surface so that the range become 2R ?
( p0=1 atm =105 Pa and g=10 m/s2)


A
1 atm
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B
2 atm
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C
4 atm
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D
3 atm
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Solution

The correct option is D 3 atm
Let us suppose extra pressure applied is p.
According to question -


For case 1 :
Velocity of efflux,
v1=2gh=2×10×10
=102 m/s ........(1)
Range of efflux,
R=v1t=102t .....(2) [ from (1) ]
For case 2 :
Range of efflux,
R2=2R=202t [ from (2) ]
v2t=202t
[ time t will be same as height of the hole is fixed ]
v2=202 m/s .......(3)
On applying Bernoulli's Equation for second case,
p0+p+ρgh=p0+12ρv22
p=12ρv22ρgh
p=12×1000×(202)21000×10×10
[ from (3) ]
p=3×105 N/m2=3 atm
[ 1 atm=105 N/m2 ]
Extra pressure of 3 atm has to be applied to make the range of efflux double.

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