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QUESTION: 1

When a body, floating in a liquid is given a small angular displacement, it starts oscillating about a point known as

Solution:

Where M is metacentre and θ is small angle of hill through which a body is tilted.

Hence metacenter is a point about which a body oscillate when tilted or given a small angular displacement.

QUESTION: 2

The time of oscillation of a floating body is given by

Where

K = Radius of Gyration of the floating body about its centre of gravity

h = Metacentric height of the floating body

Solution:

Time of oscillation of a floating body is

K = radius of gyration

h = metracentric height

QUESTION: 3

The time of oscillation of a floating body with increase in metacentric height will be

Solution:

Time of oscillation

as h increases, time of oscillation decreases

QUESTION: 4

A floating body is in stable equilibrium when

Solution:

For stable equilibrium

QUESTION: 5

A submerged body will be in stable equillibrium. if

Solution:

For stable equilibrium of submerged body:

Hence for stable equilibrium of submerged body centre of buoyancy B should be above G.

QUESTION: 6

Which one of the following is the conditions for stable equilibrium for a floating body

Solution:

For stable equilibrium

For stable equilibrium metacenter is above the center of gravity.

QUESTION: 7

How is the metacentric height (GM) expressed

Where I = Moment of inertia of the plan of the floating body at the water surface

V = Volume of the body submerged in water

BG = Distance between the center of gravity (G) and the center of Buoyancy (B)

Solution:

Metacentric height,

GM = BM - BG

Where I = Area moment of inertia of top view about longitudinal axis

V = Volume of the fluid displaced

Hence,

QUESTION: 8

An odd shaped body weighing 7.5 kg and occupying 0.01 m^{3} volume wiil be completely submerged in a fluid having specific gravity of

Solution:

QUESTION: 9

A cylindrical body of cross-sectional area A height H and density ρ_{s} is immersed to a depth h in a liquid of density ρ and tied down to bottom with a string then the tension in the string is

Solution:

w + T = F_{B} = weight of fluid displaced

QUESTION: 10

A float valve of the ‘ball-cock’ type required to close an opening of a supply pipe feeding a cistern as shown in the given figure

The buoyant force F_{B} required to be exerted by the float to keep the valve closed against a pressure of 0.28 N/mm^{2} is

Solution:

Taking moment about hinge We get

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