Q.48 Whales can dive undersea to depths of 2 km. The pressure on the whale at this depth
(ignoring atmospheric pressure) is _______ × 106 Pa. (Density of sea water = 1
g cm–3 and g =10 m s–2)
Whales Dive Pressure at 2 km Depth: Calculate 20 × 10⁶ Pa Seawater
Whales dive to 2 km depths facing extreme hydrostatic pressure from seawater, calculated as 20 × 10⁶ Pa using density 1 g cm⁻³ and g=10 m s⁻². This key CSIR NET Life Sciences physics concept tests unit conversions and P=ρgh formula application.
Problem Breakdown
Hydrostatic pressure ignores atmospheric effects and uses P = ρgh, where ρ is fluid density, g is gravity, and h is depth. Seawater density converts from 1 g cm⁻³ to 1000 kg m⁻³ by multiplying by 1000, since 1 g = 0.001 kg and 1 cm³ = 10⁻⁶ m³. Depth equals 2000 m, and g = 10 m s⁻², yielding P = 1000 × 10 × 2000 = 2 × 10⁷ Pa or 20 × 10⁶ Pa.
Step-by-Step Solution
- Convert units first: ρ = 1 g cm⁻³ = 1000 kg m⁻³.
- Substitute: P = 1000 kg m⁻³ × 10 m s⁻² × 2000 m = 20,000,000 Pa.
- Express in ×10⁶ Pa: 20,000,000 / 1,000,000 = 20.
Hydrostatic Pressure Formula
Pressure underwater builds linearly: every 10 m adds ~1 atm (10⁵ Pa) for seawater density near 1000 kg m⁻³. At 2 km (2000 m), expect 200 atm equivalents, matching 20 × 10⁶ Pa.
Unit Conversion Essentials
Seawater density 1 g cm⁻³ = 1000 kg m⁻³: 1 g/cm³ × (1 kg/1000 g) × (1 m³/10⁶ cm³) = 1000 kg m⁻³. Depth 2 km = 2000 m. Plug into P=ρgh for precise CSIR NET solving.
Whale Physiology Context
Sperm whales dive beyond 2 km, compressing lungs to manage pressure via collapsible alveoli, not rigid bodies. This adapts to 20 MPa without implosion.
Parameters Table
| Parameter | Value | Unit | Role in Calculation |
|---|---|---|---|
| Density (ρ) | 1 → 1000 | g cm⁻³ → kg m⁻³ | Mass per volume |
| Gravity (g) | 10 | m s⁻² | Acceleration |
| Depth (h) | 2 → 2000 | km → m | Vertical distance |
| Pressure (P) | 20 | ×10⁶ Pa | Final result |
