In the arrangement as shown, `A` and `B` arc two cylinders each of length `L` and density `d_1` and `d_(2)(d_(1)ltd_(2))` respectively. They are joined together and submerged in the liquid of density d with length `L//2` of `A` outside the liquid. If the difference in densities of two cylinders is equal to density of the liquid, find `d_(1)`.

Options

A. `5/4d`
B. `d/4`
C. `3/4d`
D. `d/2`

Answer

B

Explanation

Upthrust `=` Net weight
`3/2LAdg=(d_(1)+d_(2))LAg`
`impliesd_(1)=d_(2)=3/2d`
and `d_(2)-d_(1)=d`
`implies d_(2)=5/2d` and `d_(1)=d/4`