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Equal volume of two immiscible liquids of densities `rho` and `2rho` are filled in a vessel as shown in the figure. Two small holes are punched at depths `h//2` and `3h//2` from the surface of lighter liquid. If `v_(1)` and `v_(2)` are the velocities of efflux at these two holes, then `v_(1)//v_(2)` is

A

` (1)/(2sqrt2 ) `

B

` (1)/(2) `

C

` (1)/(1) `

D

` (1)/(sqrt2 ) `

Text Solution

Verified by Experts

The correct Answer is:
D
`v_(1)=sqrt(2gxxh//2)`
Applying Bernoulli’s theorem between points just inside and outside of second hole :
`P_(0)+rhogh+2rhogxx(h)/(2)=P_(0)+(1)/(2)(2rho)xxv_(2)^(2)" "Rightarrow" "v_(2)=sqrt(2gh)," ""Hence"(v_1)/(v_2)=(1)/(sqrt2)`
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