Question

As the drawing illustrates, a pond full of water has the shape of an inverted cone with the tip sliced off and has a depth of $30\, m$. The atmospheric pressure above the pond is $1.0 \times 10^{5} Pa$. The circular top surface (radius $=R_{2}$ ) and circular bottom surface (radius $=R_{1}$ ) of the pond are both parallel to the ground. The magnitude of the force acting on the top surface is the same as the magnitude of the force acting on the bottom surface. Obtain $\frac{R_{2}}{R_{1}}$.

Answer 1

$10^{5} \pi R_{2}^{2}=\left(10^{5}+30 \times 10^{3} \times 10\right) \pi R_{1}^{2}$
$10^{5} R_{2}^{2}=4 \times 10^{5} R_{1}^{2} ; \frac{R_{2}}{R_{1}}=2$