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Question

Locate the COM of a uniform hemisherical solid with respect to 0 as shown in figure. (Radius = r)


A

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B

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C

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D

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Solution

The correct option is B


Figure shows a hemisphere of mass M and radius R. To find its centre of mass (only ycoordiante), we consider an elemental disc of width dx, mass dm at a distance x from the centre of the hemisphere.This radius of this elemental disc will be given as r=R2x2

The mass dm of this disc can be given asdm=3M2πR3×πr2dx=3M2R3(R2x2)dxycm of the hemisphere is given asycm=1MR0dm x=1MR03M2πR3(R2x2)dx x=32πR3R0(R2x2)x dxycm=3R8


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