Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is _________ N.
(Given, atmospheric pressure =10⁵ Nm⁻², density of mercury =1.36 × 10⁴ kg m⁻³, g=10 m s⁻², π=22/7)

Solution

Physics sir · 3 steps

The mercury surface is open to the air, so the bottom feels the atmosphere plus the mercury column.

1. Pressure at bottom. The open top of the tube is at atmospheric pressure P₀. Going down a depth h of mercury adds ρ g h.

   F = (P₀ + ρ g h)π r²

2. Put in numbers. ρ g h = 1.36 × 10⁴ × 10 × 0.3 = 4.08 × 10⁴ N m⁻², so the total pressure is 1.408 × 10⁵ N m⁻². The area is 22/7 × (0.02)² = 1.257 × 10⁻³ m².
3. So. F = 1.408 × 10⁵ × 1.257 × 10⁻³ ≈ 177 N, so the answer is 177.

The common slip: 51. Using only the mercury column's pressure ρ g h and leaving out P₀ gives about 51 N, not 177 N.

The idea to keep. When a question gives you atmospheric pressure, it wants absolute pressure: P₀ + ρ g h. Convert cm to m before squaring the radius.

Answer from the NTA final answer key. Solution by PrepWiser.