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. `5/4d`
B. `4/5d`
C. `4d`
D. `d/5`

Answer

A

Explanation

Weight of clylinder `=` Uthrust due to upper liquid `+` Upthrust due to lower liquid
`impliesD=A/5xxLxxg=d(A/5)[3/4L]g+2d[A/5][L/4]xxg`
`:. (5d)/4`