2. A liquid that is twice as dense as water is used in a barometer. With this barometer, atmospheric pressure would push the liquid to a height of 5.15m. Explain why.\

The reason why the height for the liquid is 5.18 m is because, for constant pressure, height is inversely proportional to density.

Explanation:

We know that pressure, P = ρgh where ρ = density of material, g = 9.8 m/s and h = height.

Since density of liquid = 2 × density of water = 2 × 1000 kg/m = 2000 kg/m³

Since atmospheric pressure = 101500 N/m²,

The height of liquid for this pressure is h = P/ρg = 101500/(2000 × 9.8) = 5.18 m

For the same pressure, the height for water is h = P/ρg = 101500/(1000 × 9.8) = 10.36 m

Since pressure = constant,

P = ρgh ⇒ P/ρg = h since P and g are constant, h ∝ 1/ρ

ρ₁h₁ = ρ₂h₂

So, the reason why the height for the liquid is 5.18 m is because, for constant pressure, height is inversely proportional to density.

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