Q1. The metacentric high of a passenger ship is kept lower than that of a naval or a cargo ship because
(a) apparent weight will increase
(b) otherwise it will be in neutral equilibrium
(c) it will decrease the frequency of rolling
(d) otherwise it will sink and be totally immersed
Sol. In case of ships the shifting of cargo may cause the ships to roll. As such along with the consideration of the stability of a ships, its period of roll is also required to be determined. This so because increasing the metacentric height gives greater stability to a floating body
Q2. What is buoyant force?
(a) Lateral force acting on a submerged body
(b) Resultant force acting
(c) Resultant force due to water on a
(d) Resultant hydrostatic force on a fluid surrounding it
Sol. Buoyant force is the resultant hydrostatic force, on a body due to fluid surrounding it. The buoyant force is the force exerted on the body equal to the weight of fluid displaced by the body
Q3. Stability of a floating body can be improved by which of the following?
1 Making its width large
2 Making the draft small
3. Keeping the centre of mass low
4 Reducing its density
Select the correct answer using the codes given below:
(a) 1, 2,3 and 4
(b) 1, 2 and 3 only
(c) 1 and 2 only
(d) 3 and 4 only
Sol. Stability of a floating body can be improved by making width large which will increase I and will thus increase the metacentric height and keeping the centre of mass low and making the draft small.
Q4. The distance from the centre of buoyancy to the metacentre is given by I/Vwhere Vis the
volume of fluid displaced. What does I represent?
(a) Moment of inertia of a horizontal section of the body taken at the surface of the fluid
(b) Moment of inertia about its vertical centroidal axis
(c) Polar moment of inertia
(d) Moment of inertia about its horizontal
Sol. BM= distance between centre of buoyancy to metacentre is given by I/Vd , where Vd is volume
of fluid displaced. I is moment of Inertia of a horizontal section of a body taken at the surface of the fluid.
Q5. For floating bodies, how is the metacentric radius defined?
(a) The distance between centre of gravity and the metacentre.
(b) Second moment of area of plane of flotation about centroidal axis perpendicular to plane of rotation/immersed volume.
(c) The distance between centre of gravity and the centre of buoyancy
(d) Moment of inertia of the body about its axis of rotation/immersed volume.
Sol. Metacentric radius or metacentric height is the distance between centre of gravity and the metacentre.
Q6. Consider the following statements related to the stability of floating bodies:
1.The metacentre should be above the centre of gravity of the floating body for stable equilibrium during small oscillations.
2.For a floating body, stability is not determined simply by the relative positions of centre of gravity and centre buoyancy.
3.The position of metacentre of a floating bodyis fixed irrespective of the axis of oscillations.
4.Large value of metacentric height reduces the period of roll of the vessel.
Which of these statements are correct?
(a) 1and 3 only
(b) 2 and 4 only
(c) 1, 2 and 4 only
(d) 1, 2, 3 and 4
Sol. The position of metacentre of a floating body is, not fixed. As the axis oscillations change, its metacentre also changes.
Q8. As a ship enters into a river from sea, one can expect that
(a) It rises a little
(b) It sinks a little
(c) It remains at the same level
(d) Its level depends on the material used for construction
Sol. As a ship enters into a river from sea, one can expect that it sinks a little because of some Buoyancy force acts
Q9. Calculation of metacentric height of a floating body involves second moment of area. The axis about which this moment is to be calculated passes though the
(a) Top horizontal surface of the body
(b) Bottom horizontal surface of the body
(c) Centre of gravity of the body
(d) Centre of buoyancy
Sol. Solution – GM=(I/V)-BG
Where GM =meta centric height
I=second moment of area
V=volume of body
BG= Distance between centre of gravity
Q10. The buoyancy force is
(a) Equal to volume of liquid displace
(b) Force necessary to maintain equilibrium of a submerged body
(c) The resultant force acting on a floating body
(d) The resultant force on a body due to the fluid surrounding it
Sol. Buoyancy force is the resultant force acting on the body due to fluid surrounding it