Question

A solid cone of height $2R$ and base radius $R$ is placed over a solid hemisphere as shown in figure. Cone and hemisphere are made up of the same material. Height of center of mass of system from the ground is

• A. $\frac{5}{8}$$R$
• B. $\frac{3}{2}$$R$
• C. $\frac{17}{16}$$R$
• D. $R$

Answer 1

The correct option is C $\frac{17}{16}$$R$

$Massofhemisphericalpart,m_1=\rho \frac{2}{3}\pi R^{3}Massofconicalpart,m_2=\rho \frac{1}{3}\pi R^2\times 2R=\rho \frac{2}{3}\pi R^{3}Thus,m_1=m_2=mHeightofcentreofmassofhemisphericalpartfromground,y_1=\frac{5}{8}RHeightofcentreofmassofconicalpartfromground,y_2=R+\frac{R}{2}=\frac{3}{2}RCentreofmassofwholebody,y_{com}=\frac{m_1{y}_1+m_1{y}_1}{m_1+m_2}{y}_{com}=\frac{\frac{5}{8}R+\frac{3}{2}R}{2}=\frac{17}{16}R$