KCET · Physics · Mechanical Properties of Fluids
An aluminium sphere is dipped into water. Which of the following is true?
- A Buoyancy in water at \( 0^{\circ} \mathrm{C} \) will be same as that in water at \( 4^{\circ} \mathrm{C} \)
- B Buoyancy will be less in water at \( 0^{\circ} \mathrm{C} \) than that in water at \( 4^{\circ} \mathrm{C} \)
- C Buoyancy may be more or less in water at \( 4^{\circ} \mathrm{C} \) depending on the radius of the sphere
- D Buoyancy will be more in water at \( 0{ }^{\circ} \mathrm{C} \) than that in water at \( 4{ }^{\circ} \mathrm{C} \)
Answer & Solution
Correct Answer
(B) Buoyancy will be less in water at \( 0^{\circ} \mathrm{C} \) than that in water at \( 4^{\circ} \mathrm{C} \)
Step-by-step Solution
Detailed explanation
As buoyancy at \(0^{\circ} \mathrm{C}, \mathrm{F}_{\mathrm{b}}=\mathrm{V} \rho_{0} \mathrm{~g}\) and buoyancy at \(4^{\circ} \mathrm{C}, \mathrm{F}_{\mathrm{b}}^{\prime}=\mathrm{V} \rho_{4} \mathrm{~g}\)
\(\frac{F_{b}}{F_{b}^{\prime}}=\frac{\rho_{0}}{\rho_{4}}<1\) (density of water at \(4^{\circ} \mathrm{C}\) is maximum)
i.e., \(\mathrm{F}_{\mathrm{b}}<\mathrm{F}_{\mathrm{b}}^{\prime}\)
\(\frac{F_{b}}{F_{b}^{\prime}}=\frac{\rho_{0}}{\rho_{4}}<1\) (density of water at \(4^{\circ} \mathrm{C}\) is maximum)
i.e., \(\mathrm{F}_{\mathrm{b}}<\mathrm{F}_{\mathrm{b}}^{\prime}\)
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