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 × 105 Pa. The circular top surface (radius =R2 ) and circular bottom surface (radius =R1 ) 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 (R2/R1).

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 × 105 Pa. The circular top surface (radius =R2 ) and circular bottom surface (radius =R1 ) 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 (R2/R1). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

105 π R22=(105+30 × 103 × 10) π R12 105 R22=4 × 105 R12 ; (R2/R1)=2

105πR22​=(105+30×103×10)πR12​ 105R22​=4×105R12​;R1​R2​​=2

$1 0^{5} π R_{2}^{2} = (1 0^{5} + 30 \times 1 0^{3} \times 10) π R_{1}^{2}$
$1 0^{5} R_{2}^{2} = 4 \times 1 0^{5} R_{1}^{2}; \frac{R _{2}}{R _{1}} = 2$