Water is filled in a cylindrical container to a height of `3m`. The ratio of the cross-sectional area of the orifice and the beaker is `0.1`. The square of the speed of the liquid coming out from the orifice is `(g=10m//s^(2))`.
A
`50 m^(2)//s^(2)`
B
`50.5m^(2)//s^(2)`
C
`51m^(2)//s^(2)`
D
`52 m^(2)//s^(2)`
Text Solution
Verified by Experts
The correct Answer is:
A
Applying continuity equation at 1 and 2, we have `A_(1)v_(1)=A_(2)v_(2)`...(i) Further applying Bernoulli's equation at these two points, we have `p_(0)+rho gh +(1)/(2) rho v_(1)^(2)=p_(0)+0+(1)/(2) rho v_(2)^(2)`...(ii) Solving Eqs. (i) and (ii), we have `v_(2)^(2)=(2gh)/(I-(A_(2)^(2))/(A_(1)^(2)))` Substituting the values, we have `v_(2)^(2)=(2xx10xx2.475)/(1-(0.1)^(2))=50m^(2)//s^(2)`.
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