how to calculate centre of mass of solid hemisphere
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The region in the first quadrant enclosed by the curve y=b(a2−x2)1/2ay=b(a2−x2)1/2a and the lines y=0y=0, x=0x=0, x=kax=ka (0<k≤1)(0<k≤1), is rotated through four right angles about the xx-axis to form a solid of revolution. Show that the volume of the solid is 13πab2k(3−k2)13πab2k(3−k2).
If this solid is of uniform density find the coordinates of its centre of mass.
By considering the case b=ab=a, k=1k=1, show that the centre of mass of a uniform solid hemisphere of radius aa is at a distance 38a38afrom the centre.
If this solid is of uniform density find the coordinates of its centre of mass.
By considering the case b=ab=a, k=1k=1, show that the centre of mass of a uniform solid hemisphere of radius aa is at a distance 38a38afrom the centre.
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