Question:
A tub is filled with water and a wooden cube \(10\,\text{cm} \times 10\,\text{cm} \times 10\,\text{cm}\) 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 \(=1\,\text{g/cm}^3\) and density of wood as \(0.4\,\text{g/cm}^3\)).}
A tub is filled with water and a wooden cube \(10\,\text{cm} \times 10\,\text{cm} \times 10\,\text{cm}\) 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 \(=1\,\text{g/cm}^3\) and density of wood as \(0.4\,\text{g/cm}^3\)).}
Updated On: Apr 10, 2026
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Correct Answer: 387
Solution and Explanation
Concept:
According to Archimedes’ principle, the weight of the floating body equals the weight of displaced water.
When the coin is placed on the cube, the additional submerged volume corresponds to the weight of the coin.
Step 1:Find additional displaced volume} Base area of cube: \[ A = 10 \times 10 = 100 \,\text{cm}^2 \] Increase in submerged height: \[ \Delta h = 3.87 \,\text{cm} \] Additional displaced volume: \[ \Delta V = A \times \Delta h \] \[ \Delta V = 100 \times 3.87 \] \[ \Delta V = 387 \,\text{cm}^3 \]
Step 2:Use Archimedes principle} Mass of displaced water equals mass added (coin): \[ m = \rho \Delta V \] \[ \rho = 1 \,\text{g/cm}^3 \] \[ m = 1 \times 387 \] \[ m = 387 \,\text{g} \] Thus \[ \boxed{387} \]
Step 1:Find additional displaced volume} Base area of cube: \[ A = 10 \times 10 = 100 \,\text{cm}^2 \] Increase in submerged height: \[ \Delta h = 3.87 \,\text{cm} \] Additional displaced volume: \[ \Delta V = A \times \Delta h \] \[ \Delta V = 100 \times 3.87 \] \[ \Delta V = 387 \,\text{cm}^3 \]
Step 2:Use Archimedes principle} Mass of displaced water equals mass added (coin): \[ m = \rho \Delta V \] \[ \rho = 1 \,\text{g/cm}^3 \] \[ m = 1 \times 387 \] \[ m = 387 \,\text{g} \] Thus \[ \boxed{387} \]
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