Question

A circular window 30 cm in diameter in a submarine can withstand a maximum force, exerted by the fluids surrounding it, of 5.20 × 105 N without damage. What is the maximum depth in a fresh-water lake to which the submarine, containing air at atmospheric pressure, can go without damaging the window? The density of fresh water is 1000 kg/m3.

Answer 1

Answer:

755 m

Explanation:

Given:

Diameter of the window, d = 30 cm

                                            = 0.3 m

Therefore, radius r = 0.15 m

Force, F = $5.2\times 10^{5}N$

Density, ρ = 1000kg/m3

Thus, Area of the window, A = $\pi \times r^{2}$

                                               = $3.14 \times 0.15^{2}$

                                               = 0.07 $m^{2}$

Therefore pressure, P = Force / Area

                                    = $5.2\times 10^{5}N$ /  0.07

                                    = $7.4 \times 10^{6}$

We know that, pressure, P = ρ.g.h

where, g is acceleration due to gravity = $9.8 m/s^{2}$

            h is depth

Therefore,  P = ρ.g.h

            or h = $\frac{P}{\rho \times g}$

                    = $\frac{7.4\times 10^{6}}{1000\times 9.8}$

                    = 755 m

Thus the maximum depth is 755 meter.