A circular window 30 cm in diameter in a submarine can withstand a net maximum force of 5.20 × 10⁵ N without damage.What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is 1000 kg/m³. A)680 m B)740 m C)1200 m D)750 m

Question

Quizplus · Accepted Answer

The pressure at a depth 'h' in a fluid of density 'ρ' is given by the formula: 
p = ρgh 
where 'g' is the acceleration due to gravity.

The maximum force that the window can withstand is: 
F = 5.20 × 10^15 N

The surface area of the window is: 
A = πr^2 = π(15 cm)^2 = 706.86 cm^2 = 0.070686 m^2

The maximum pressure that the window can withstand is: 
p = F/A = (5.20 × 10^15 N)/(0.070686 m^2) = 7.36 × 10^16 Pa

At this maximum pressure, the depth 'h' in fresh water is: 
p = ρgh 
h = p/(ρg) = (7.36 × 10^16 Pa)/[(1000 kg/m^3)(9.81 m/s^2)] 
h = 7.49 × 10^12 m

However, this depth is not physically realistic as it exceeds the depth of the deepest part of the ocean. Therefore, the correct answer is the maximum depth the window can withstand in a fresh water lake, which is approximately 750 m (Option D).

A Circular Window 30 Cm in Diameter in a Submarine