Equal volumes of two immiscible liquids of densities `rho` and `2 rho` are filled in a vessel as shown in figure. Two small holes are punvhed 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

Options

A. ` (1)/(2sqrt2 ) `
B. ` (1)/(2) `
C. ` (1)/(1) `
D. ` (1)/(sqrt2 ) `

Answer

D

Explanation

`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)`