Find the centre of mass of an annular half disc shown in figure.
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Sol. Let ρ be the mass per unit area of the object. To find its centre of mass we consider an element as a half ring of mass dm as shown in figure of radius r and width dr and there we have
Now dm = ρπ r dr
Centre of mass of this half ring will be at 
y cm = 
y cm = 
= 
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