A cylindrical block of length 2l is made of two different materials. The upper half has density `d_(1)` and and lower half, which is heavier, has density `d_(2)` the block is floating in a liquid of unknown density d with `(l)/(2)` of its length outside the liquid.
(a) Find d
(b) Show that `dgt(4d_(1))/(3)`

Options

A. `d_(1)gt(3)/(4)d`
B. `(d)/(2)gtd_(1)`
C. `(d)/(4)gtd_(1)`
D. `dltd_(1)`

Answer

A

Explanation

`m_(1)g+m_(2)g` =Buyonany
`ALd_(1)g+ALd_(2)g=(3)/(4)xxLAdg`
`d_(1)+d_(2)=(3)/(2)d" "implies" "d_(1)gtd_(2)`
`2d_(1)gtd_(1)+d_(2)" "implies " "2d_(1)gt(3)/(2)dimpliesd_(1)gt(3)/(4)d`