Location of centre of gravity of a hemisphere, Mechanical Engineering

Location of centre of gravity of a hemisphere:

Find out the location of centre of gravity of a hemisphere of radius a.

Solution

Figure shows the cross-section of the hemisphere where DE = 2a, the diameter of the hemisphere.

1117_Location of centre of gravity of a hemisphere2.png

Assume a thin slice AB of volume dV taken at a distance x from center O of the hemisphere.

Radius of slice = a sin θ

If dx is the small thickness of slice,

dV = π (a sin θ)2  dx

x = a cos θ

dx = - a sin θ dθ

Letting equation of moments about O,

1143_Location of centre of gravity of a hemisphere.png

343_Location of centre of gravity of a hemisphere1.png

                                    = πa4/4

                            ∴x¯ =3a/8

Posted Date: 1/29/2013 1:06:14 AM | Location : United States







Related Discussions:- Location of centre of gravity of a hemisphere, Assignment Help, Ask Question on Location of centre of gravity of a hemisphere, Get Answer, Expert's Help, Location of centre of gravity of a hemisphere Discussions

Write discussion on Location of centre of gravity of a hemisphere
Your posts are moderated
Related Questions
Q. Can you explain Investment casting? -Investment casting produces very high surface quality and dimensional accuracy. -Investment casting is commonly used for precision eq

SHIELDING GAS The primary function of the shielding gas is to exclude the atmospheric air from the arc zone. However, the shielding gas has significant influence on the arc cha

Plastic material and rigid plastic material: For the plastic material, there is stress at which plastic deformation begins. A rigid plastic material is one in which the ela

Q. Show the Procedure of Compute flange stresses? Compute flange stresses and the actual bolt stress using: - COLT values for gasket seating stress, ‘y' and the gasket facto

Introduction There was a power point presentation on Hydrogen fuel, Hydrogen production using electrolyzer and solar energy and solar energy.Topics like Alternative Energy Sys

Rankine cycle with respect to P-V, T diagrams: The steam having high pressure is expanded to a low pressure within a reciprocating engine or a turbine. If expansion is idea

Direct and Bending Stresses: defined neutral axis, introduced the influence of axial force and bending moment on different sections, attained the core or kernel of di

Q. Define the project scope? The Design Basis Memorandum defines the project scope. This includes basic design concepts and the basis and philosophies upon which the project s

simply supported beam subjected to point loads results

state a note on reversible and irreversible process?