JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Fluid Mechanics

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a 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?
(Given : density of water

= 1000 kg m^{- 3}

)

(A) $1400 cm^{3}$
(B) $4000 cm^{3}$
(C) $400 cm^{3}$
(D) $600 cm^{3}$ ✓ Correct

Answer: (D)

Solution

For a floating body, weight equals the buoyant force from the displaced water:

M g = ρ_{w a t er} V_{d} g

Given

M = 400 g = 0.4 kg

and

ρ_{w a t er} = 1000 kg/m^{3}

V_{d} = \frac{M}{ρ _{w a t er}} = \frac{0.4}{1000} = 4 \times 1 0^{- 4} m^{3} = 400 cm^{3}

The total volume of the cube (edge 10 cm) is

V_{t o t a l} = (10)^{3} = 1000 cm^{3}

The volume outside the water is

V_{o u t s i d e} = V_{t o t a l} - V_{d} = 1000 - 400 = 600 cm^{3}

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option

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