Question

On a day when the atmospheric pressure at the surface of the water is 1.03×10^5 Pa, at what depth below the surface of the water is the absolute pressure twice the pressure at the surface?

a) 5 m
b) 10 m
c) 15 m
d) 20 m

Answer 1

The depth at which the absolute pressure is twice the atmospheric pressure of 1.03×105 Pa is 10 meters below the surface of the water.

Step-by-step explanation:

To determine at what depth below the surface of the water the absolute pressure is twice the atmospheric pressure, we must first consider the atmospheric pressure at the surface, which is given as 1.03×105 Pa. Using the principle that the pressure increases with depth due to the weight of the water column above, we can use the formula P = P0 + ρgh, where P is the absolute pressure at depth, P0 is the atmospheric pressure, ρ is the density of water (approximately 1000 kg/m3), g is the acceleration due to gravity (9.81 m/s2), and h is the depth in meters. To find the depth at which the pressure is twice the atmospheric pressure, the equation becomes 2P0 = P0 + ρgh. Solving for h, we get h = P0 / (ρg). Substituting the known values, h = (1.03×105 Pa) / (1000 kg/m3 × 9.81 m/s2) which gives us approximately 10 meters depth. Therefore, the correct answer is b) 10 m.