Engineering Mechanics

Chapter 36 : Equilibrium of Floating Bodies „„„„„ 757

For stable equilibrium, the metacentre (M) should be above G or may coincide with G.

i.e., BGñBM

OG – OBñBM

0.75 – 0.75 lñ0.27 l

1.02 lñ0.75

lñ0.735 m

Now volume of water displaced,

= 0.377 (0.735)^3 = 0.15 m^3

This should be equal to the weight of the buoy, therefore weight of the buoy,

W= 0.15 × 9·8 = 1·47 kN Ans.

EXERCISE 36.2

1. A cylindrical block of wood of specific gravity 0.8 has a diameter of 24 cm. What is the
   maximum permissible length of the block, in order that it may float vertically in water?
   [Ans. 21.2 cm]


2. A cylinder has diameter of 45 cm and of specific gravity 0.9. Find the maximum permis-
   sible length of the cylinder, so that it can float with its axis vertical. [Ans. 53 cm]


3. A wooden cylinder of circular section and of specific gravity 0.6 is required to float in an
   oil of specific gravity 0.8. If the diameter of the cylinder is d, and its length l, show that l
   cannot exceed 0.817 d, for the cylinder to float with its longitudinal axis vertical.


4. A uniform wooden circular cylinder of 40 cm diameter and of specific gravity 0.6 is
   required to float in specific gravity 0.8. Find the maximum length of the cylinder, in order
   that it may float vertically in water. [Ans. 32.7 cm]


5. A solid cylinder is made up of two materials. Its base for 5 cm length is of some material
   of specific gravity 4 and the remaining portion of material of specific gravity 0.4. Find the
   maximum length of the cylinder, so that it may float in water with its axis vertical.
   [Ans. 86 cm]


6. A wooden cone of mass 700 kg/m^3 is required to float in water, with its axis vertical.
   Determine the least apex angle, which shall enable the cone to float in stable equilibrium.
   [Ans. 30° 48′]

QUESTIONS

1. State the Law of Archimedes and explain its application in buoyancy.


2. Define the terms
   (a) centre of buoyancy,
   (b) metacentre, and
   (c) metacentric height.


3. Derive an equation for the metacentric height of a floating body.


4. Explain the types of equilibrium.


5. How will you find the least apex angle of a conical buoy so that it may float in water?