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

Considering vertical equilibrium of cylinder weight of cylinder `=` upthrust due to upper liquid `+` upthrust due to lower liquid
`:. (A//5)(L)Dg=(A//5) (3L//4)(d)g+ (A//5 )(L//4)(2d)/(g)`
`becauseD=((3)/(4))d+((1)/(4))(2d)`
`D=(5)/(4)d`