JEE Main 2026 — Apr 2, Shift 1 — Physics solution

JEE Main2026Apr 2, Shift 1Physics

A tube is filled with water and a wooden cube $10$ cm $\times 10$ cm $\times 10$ cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87$ cm. The mass of the metal coin is ____ gram.

(Take water density as $1$ g/cm $^{3}$ and density of wood as $0.4$ g/cm $^{3}$ )

Your answer

Solution

Placing the coin increases the submerged depth by $Δ h = 3.87$ cm. The extra buoyant force generated equals the weight of the coin (the wood density is irrelevant to the additional submersion).

$m_{c} g = ρ_{water} \cdot V_{add} \cdot g$

$m_{c} = ρ_{water} \cdot A_{cube} \cdot Δ h = (1 g/cm^{3}) (10 \times 10 cm^{2}) (3.87 cm)$

$m_{c} = 387$ g

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