A carpenter has constructed a toy as shown in | vedclass

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(C) Let $d$ be the density of the material of the cone and $12d$ be the density of the sphere.The mass of the cone is given by:$m_c = \frac{1}{3} \pi

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at a distance $4R$ from $O$

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(C) Let $d$ be the density of the material of the cone and $12d$ be the density of the sphere.The mass of the cone is given by:$m_c = \frac{1}{3} \pi (2R)^2 (4R) d = \frac{16}{3} \pi R^3 d$The center of mass of the cone $C_1$ is at a height $y_c = \frac{4R}{4} = R$ from $O$.The mass of the sphere is given by:$m_s = \frac{4}{3} \pi R^3 (12d) = 16 \pi R^3 d = 3m_c$The center of mass of the sphere $C_2$ is at a height $y_s = 4R + R = 5R$ from $O$.The center of mass of the toy $y_{cm}$ is given by:$y_{cm} = \frac{m_c y_c + m_s y_s}{m_c + m_s}$$y_{cm} = \frac{m_c (R) + 3m_c (5R)}{m_c + 3m_c} = \frac{16 m_c R}{4 m_c} = 4R$ from $O$.

$A$ carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of the cone,the position of the centre of mass of the toy is given by

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