The barometric reading at a place is 73.5m Hg. Calculate the pressure at a point 30m below the surface of…

The question has typos: the barometric reading should be 73.5 cm Hg (not m), and the density of mercury is given as 1.2 x 10⁴ kg/m³ (the real value is 1.36 x 10⁴). I'll work with the values given.

Concept

Total pressure at depth = atmospheric pressure + pressure due to the water column:

P = P_atm + ρ_w g h

Step 1: Atmospheric pressure

Using h = 73.5 cm = 0.735 m, ρ = 1.2 x 10⁴ kg/m³ and g = 10 m/s²:

P_atm = ρgh = 1.2 x 10⁴ x 10 x 0.735 = 8.82 x 10⁴ N/m²

Step 2: Pressure from 30 m of water

ρ_w g h = 1.0 x 10³ x 10 x 30 = 3.0 x 10⁵ N/m²

Step 3: Total pressure

P = 3.0 x 10⁵ + 0.882 x 10⁵ = 3.882 x 10⁵ N/m² ≈ 3.9 x 10⁵ N/m²

This is closest to 4.0 x 10⁵ N/m², which is option A.

Checking the other options

• Option B (3.0 x 10⁵) would be the water pressure alone, with atmospheric pressure left out.
• Options C and D are too small, because the water column alone already gives 3.0 x 10⁵.

Tip: In "pressure at depth" questions, always add atmospheric pressure to ρgh unless the question asks for gauge pressure. When reading the barometer, convert cm Hg to m before using ρgh. Also check the options first. Here, 3.0 x 10⁵ is just the water part, so the answer must be a bit above it, which leaves 4.0 x 10⁵.