A homogeneous solid cylinder of length L(LltH/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure `P_0`. Then density D of solid is given by

Options

A. ` (5)/(4) d `
B. ` (4)/(5) d `
C. ` 4d `
D. ` (d)/(3) `

Answer

A

Explanation

Weight of cylinder = Upthrust due to upper liquid + upthrust due to lower liquid
`rArrD((A)/(5))xxLxxg=d((A)/(5))[(3)/(4)L]g+2d[(A)/(5)][(L)/(4)]xxg" "therefore" "D=5d//4`