A submarine is at a depth of 500 m under the water. The force on a circular hatch of diameter 1.00 m due to the seawater (density = 1,025 kg/m³) pressure from outside the submarine is A) 2.45 × 10⁶ N. B) 4.02 × 10⁶ N. C) 3.94 × 10⁶ N. D) 5.50 × 10⁶ N. E) 6.34 × 10⁶ N.

Question

Quizplus · Accepted Answer

The force on the hatch can be calculated using the formula for pressure due to a fluid column, $P = \rho gh$, and then applying the force equation $F = PA$, where $P$ is the pressure, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), $h$ is the depth, $F$ is the force, and $A$ is the area of the hatch. The area of a circle is given by $A = \pi r^2$, where $r$ is the radius of the circle. Given that the diameter of the hatch is 1.00 m, the radius is 0.5 m. Therefore, the area is $A = \pi (0.5)^2 = 0.785 \, \text{m}^2$. The pressure at 500 m depth is $P = 1025 \times 9.8 \times 500$. The force is then $F = P \times A$. Plugging in the numbers, we get a force close to $4.02 \times 10^{6} \, \text{N}$, which matches choice B.

A Submarine Is at a Depth of 500 M Under