Question

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

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

Answer 1

Correct Answer - A
Weight of cylinder = upthrust due to both liquids
`V xx D xx g = ((A)/(5)*(3)/(4)L) xx d xx g + ((A)/(5)*(L)/(4)) xx 2d xx g`
`implies ((A/5)*L)D*g = (Ald g)/(4) implies D/5 =d/4 :. D = 5/4 d` .