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
If Battery Discharges Frequently Causes of Problem Remedy Electrolyte specific gravity NG Charging not done fully

Q. What do you mean by Alloys? Metallic materials that contain alloying elements, including chromium (Cr), cobalt (Co), Columbium or niobium (Cb or Nb), copper (Cu), iron (Fe),

a) Define various types of chips and factors responsible for their formation with diagram b) Describe cutting ratio, shear plane and shear angle. c) Sketch Merchant circle di


ROTARY CONVERTERS Historically, these type of power sources were developed first for arc welding applications and even now these types are popular. These rotary converters are of

Find the maximum shear stress - stepped circular bar: A stepped circular bar ABC 4 m long fixed at one of the end 'A' is subjected to a torque of 10 kN-m. If the portion AB is

SHIELDED METAL ARC WELDING (SMAW) It also known as Manual Metal Arc Welding (MMAW). The heat required for welding is generated by the electric arc formed between metallic elect

Wet saturated steam -  thermodynamics: we t saturated steam Wet steam is a 2-phase mixture comprising of boiling water particles and dry steam in equilibrium state. Its for


Determine maximum internal diameter of hollow shaft: A solid shaft of mild steel which is 200 mm in diameter is to be replaced by hollow shaft of alloy steel for which the al