Question

A uniform solid right circular cone of base radius r is joined to a uniform solid hemisphere of radius r and of the same density, so as to have a common face. The centre of mass of the composite solid lies on the common face. The height of the cone is –

• A. 2r
• B. 4r
• C. 3r
• D. r$\sqrt{6}$

Answer 1

Answer: (B)

4r

Answer 2

y_cm = $\frac{m_{1}x_{1} + m_{2}x_{2}}{m_{1} + m_{2}}$, m₁ = r$\frac{1}{3}$p r²h

m₂ = r$\left( \frac{2}{3}\pi r^{3} \right)$, 0 =$\frac{m_{1}\frac{h}{4}–m_{2}\frac{3r}{8}}{m_{1} + m_{2}}$, h = $\sqrt{3}$r

TE = KE + PE = $\frac{1}{2}$mv² + $\frac{1}{2}$Kx²