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A homogeneous solid cylinder of length L...

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`

Text Solution

Verified by Experts

The correct Answer is:
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` .
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