A cubical block of density ρᵦ = 600 kg/m³ floats in a liquid of density ρₑ = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part is ___

A cubical block of density ρb = 600 kg/m³ floats in a liquid of density ρe = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part is

Q. A cubical block of density ρ_b = 600 kg/m³ floats in a liquid of density ρ_e = 900 kg/m³. If the height of block is H = 8.0 cm then height of the submerged part is ____ cm.

(A) 6.3

(B) 4.3

(D) 5.3

Correct Answer: 5.3 cm

Explanation

When a body floats in a liquid, the buoyant force acting on it is equal to its weight.

According to Archimedes’ principle,

Weight of block = Weight of liquid displaced

ρ_b V g = ρ_e V_sub g

Here V is the total volume of the block and V_sub is the volume of the submerged part.

Canceling g from both sides,

ρ_b V = ρ_e V_sub

Since the block is cubical, volume is proportional to height.

ρ_b H = ρ_e h

Substitute the given values:

600 × 8 = 900 × h

h = (600 / 900) × 8

h = (2 / 3) × 8

h = 5.33 cm

Hence, the height of the submerged part of the block is 5.3 cm.

Explanation

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