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 ) /(4) d `
B. ` (d ) /(4) `
C. ` (3 )/ (4) d `
D. ` (d)/(2) `

Answer

B

Explanation

` d = d _ 2 - d _ 1 " " `…(i)
` (L xx A xx d _1 + L xx A xx d _ 2 ) g = A xx L xx d xx g + A xx (L)/(2) xx d xx g `
` d _ 1 + d _ 2 = (3)/(2) d rArr 2 d _ 2 = (5)/(2) d , d _ 2 = (5)/(4) d, d _ 1 = (3)/(2) d - (5 d ) /(4 ) = (d)/(4 ) `