A solid hemisphere and a solid cone have a common base. The centre of mass of common structure coincides with the common base. If R is the radius of hemisphere and h is the height of the cone, then $\frac{h}{R}$ will be $\sqrt{k}$ . Then the value of $k$ is_______

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answer is 3.

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Detailed Solution

$m_{1} = k \times \frac{1}{3} π R^{2} h, y_{1} = \frac{h}{4}$
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$m_{2} = k \times \frac{2}{3} π R^{3}, y_{2} = \frac{- 3 R}{8}$
$y_{C . M} = \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}} = 0$
$\frac{h}{R} = \sqrt{3}$

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