question_answer

Two non-mixing liquids of densities \[\rho  and \]\[n\rho  \left( n > 1 \right)\]are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p < 1) in the denser liquid. The density d is equal to:

A) \[\left\{ 1+\left( n+1 \right)p \right\}\rho \]     

B) \[\left\{ 2+\left( n+1 \right)p \right\}\rho \]

C) \[\left\{ 2+\left( n-1 \right)p \right\}\]      

D)   \[\left\{ 1+\left( n-1 \right)p \right\}\rho \]

Correct Answer: D

Solution :

[d] Weight of cylinder \[{{U}_{1}}+{{U}_{2}}\] AdLg = A (L - pL) pg + ApLnpg d = p (l - p) + npp = p - pp + npp = p [1 + np - p] = p [1+p (n - 1)]