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Diagrammatically show meta centre, centre of gravity and centre of buoyancy when the floating body is at equilibrium and when external angular displacement is applied on it.

Important Questions on Fluid Mechanics

EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A piece of ice floats in a liquid. What will happen when it melts.
MEDIUM
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
What is meta centre? What will be the position of metacentre with respect to centre of gravity in different conditions of stability of a floating body?
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A solid sphere of radius R and density ρ is attached to one end of massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement (s) is (are)
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A ball floats on the surface of water in a container exposed to the atmosphere. Will the ball remain immersed at its initial depth or will it sink or rise somewhat it the container is shifted to the moon?
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
Does the position of the Metacenter depend on the position of the center of gravity?
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
For a partially submerged body to be in unstable equilibrium, its metacentre should lie below its centre of gravity. 
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
What is meta Centre and metacentric height?
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body

A uniform narrow tube is bent into a circle of radius R and it lies in a vertical plane. Two liquids of equal volume and having densities ρ  and σ ρ > σ  fill the half tube. θ  is the angle as shown in figure. Then

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EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
For a floating body, slight angular displacement can produce oscillation about a point, this point is referred to be _____.
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A ball is made of a material of density ρ where ρoil<ρ<ρwater  with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
When the metacentre is below the centre of gravity the body is said to be in?
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
If the centre of gravity of the body lies above the metacentre, then the body is said to be in _____.
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Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body

A body, partially submerged in a liquid will be in stable equilibrium, if its metacentre:

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Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A necklace weighs 50 g In air, but it weighs 46 g in water. Assume that copper is mixed with gold to prepare the necklace. Find how much copper is present in it. (Specific gravity of gold is 20 and that of copper is 10.)
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, form a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
What is metacentre of a floating body?
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A hollow cylinder of mass m made heavy at its bottom is floating vertically in water. It is tilted from its vertical position through an angle θ and is left. The restoring force acting on it is
HARD
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
A uniform rod of density ρ is placed in a wide tank containing a liquid of density ρ0(ρ0>ρ). The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position, the rod makes an angle θ with the horizontal. Then,
MEDIUM
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
What do you mean by the metacentre of a floating body?
EASY
Physics>Mechanics>Fluid Mechanics>Condition for Equilibrium of a Floating Body
How do you find the Metacenter?