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







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