Question

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 punched at depth 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_(2))/(v_(1)))^(2)` is

Answer 1

Correct Answer - 2

Answer 2

 Answer can be found using Toricelli's law and Bernoulli's theorem

Answer 3

Given \(h_1 = \frac h2\)

and \(h_2 = \frac {3h}2 - \frac h2\)

\(h_2 = h\)

Now, we have the velocity of flux from first hole is 

\(v_1 = \sqrt{2n_1g}\)

\(v_1 = \sqrt{2\times \frac h2\times g}\)

\(v_1 = \sqrt{h g}\)

Velocity of flux from second hole is

\(v_2 = \sqrt {2h_2g}\)

\(v_2 = \sqrt {2hg}\)

Then 

\(\frac{v_1}{v_2} = \frac{\sqrt {hg}}{\sqrt{2hg}}\)

\(\frac{v_1}{v_2} = \frac1{\sqrt 2}\) 

\(\left(\frac{v_2}{v_1}\right)^2 = \left(\frac{\sqrt 2}1\right)^2\) 

\(= 2\)