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A uniform solid hemisphere of radius r is joined to uniform solid right circular cone of base of radius r. Both have same density. The centre of mass of the composite solid lies on the common face. The height (h) of the cone is

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$\sqrt{3} r$

$r \sqrt{6}$

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{3}{8} r \cdot ρ \frac{2}{3} {πr}^{3} = \frac{h}{4} \cdot ρ \frac{1}{3} {πr}^{2} h \\ \Rightarrow h = \sqrt{3} r \end{array}$

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