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Questions  

A homogeneous solid cylinder of length L<H2, cross-sectional area A5 is immersed such that it floats with its axis vertical at the liquid interface with length L4 in the denser liquid as shown in Figure. The lower density liquid is open to atmosphere having pressure P0. Then, density D of solid is given by

a
54d
b
45d
c
4d
d
d5

detailed solution

Correct option is A

Considering vertical equilibrium of cylinder, we get Weight  of  cylinder = Upthrust due  to upper  liquid + Upthrust due  to lower  liquid  ⇒A5(L)Dg=A53L4(d)g+A5L4(2d)(g)⇒D=34d+14(2d)⇒D=54d

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