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Question
An aluminium sphere is dipped into water. Which of the following is true?
Options
Buoyancy will be less in water at 0°C than that in water at 4°C.
Buoyancy will be more in water at 0°C than that in water at 4°C.
Buoyancy in water at 0°C will be same as that in water at 4°C.
Buoyancy may be more or less in water at 4°C depending on the radius of the sphere.
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Solution
Buoyancy will be less in water at 0°C than that in water at 4°C.
Explanation:
Let volume of the sphere is V and ρ is its density, then we can write buoyant force
F = VρG .....(g = acceleration due to gravity)
⇒ F ∝ ρ .....(∵ V and g are almost constant)
⇒ `F_(4^circC)/F_(0^circC) = ρ_(4^circC)/ρ_(0^circC) > 1` .....(∵ ρ4°C > ρ0°C)
⇒ `F_(4^circC) > F_(0^circC)`
Hence, buoyancy will be less in water at 0°C than that in water at 4°C.
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