Two cylinders of same cross-section and length L but made of two different materials of densities `d_(1)` and `d_(2)` are cemented together to from a cylinder of length 2L. The combination floats in a liquid of density `d " " d_(1) lt d_(2)` then

Options

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

Answer

A

Explanation

Weight of combined cylinder = upthrust

`d_(1)Lag+d_(2)Lag=d((3L)/(2))Ag implies d_(1)+d_(2)=(3)/(2)d` ltbtgt But since `d_(1) lt d_(2) implies d_(1) lt (3)/(4) d`