A rock is suspended by a light string. When the rock is in air, the tension...

A rock is suspended by a light string. When the rock is in air, the tension in the string is 52.9 N . When the rock is totally immersed in water, the tension is 32.6 N . When the rock is totally immersed in an unknown liquid, the tension is 14.4 N .

What is the density of the unknown liquid?

Solutions

Expert Solution

Gravitational acceleration = g = 9.81 m/s²

Density of water = ₁ = 1000 kg/m³

Density of the unknown liquid = ₂

Weight of the rock = Tension in the string when the rock is air = W = 52.9 N

Volume of the rock = V

Buoyant force on the rock when immersed in water = F₁ = ₁Vg

Tension in the string when the rock is immersed in water = T₁ = 32.6 N

When the rock is immersed in water the tension in the string and the buoyant force on it supports the weight of the rock.

W = F₁ + T₁

W = ₁Vg + T₁

52.9 = (1000)(9.81)V + 32.6

V = 2.0693 x 10^-3 m³

Buoyant force on the rock when it is immersed in the unknown liquid = F₂ = ₂Vg

Tension in the string when the rock is immersed in unknown liquid = T₂ = 14.4 N

When the rock is immersed in the unknown liquid the tension in the string and the buoyant force on it supports the weight of the rock.

W = F₂ + T₂

W = ₂Vg + T₂

52.9 = ₂(2.0693x10^-3)(9.81) + 14.4

₂ = 1896.56 kg/m³

Density of the unknown liquid = 1896.56 kg/m³

genius_generous answered 1 month ago

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