A solid cone of uniform density and height \( 2 R \) and base radius \( R \) has a conical porti...
0A solid cone of uniform density and height \( 2 R \) and base radius \( R \) has a conical portion scooped out from its base with the same base radius but height \( R \) as shown in the figure. The solid cone is floating in a liquid of density \( \rho \) with vertex \( A \) touching the fluid surface. If
atmospheric pressure is \( P_{0} \), the force acting on the surface \( B C D \) due to liquid is :
(a) \( \frac{\pi R^{3} \rho g}{3}\left[5+\frac{3 P_{o}}{R \rho g}\right] \)
(b) \( \frac{\pi R^{3} \rho g}{3}\left[2+\frac{P_{o}}{R \rho g}\right] \)
- (c) \( \frac{\pi R^{3} \rho g}{2}\left[5+\frac{P_{0}}{R \rho g}\right] \)
(d) \( 2 \pi R^{3} \rho g\left[5+\frac{P_{0}}{R \rho g}\right] \)
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