Question

A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity=6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.

(a) It will float

(b) It will not float

(c) Data insufficient

(d) None of the mentioned

I got this question in a job interview.

This intriguing question originated from Conditions of Equilibrium of a Floating and Submerged Bodies topic in chapter Buoyancy and Floatation of Fluid Mechanics

Answer 1

The correct option is (a) It will float

The best I can explain: AG=(weight of base*distance of C.G from base  point A) + (weight of upper part*distance of C.G from point A)/ )weight of base + weight of upper part)

                   = 14.52

By principle of buoyancy,

Weight of cylinder = Weight of water displaced

h=38.625

AB=19.31

BG=14.25-19.31= -4.79

GM= Metacentric height=I/∀ -BG

      = 6.16

As metacentric height is positive, it will float.