First slide

Fluid statics

Question

An aluminium sphere is dipped into water. Which of the following statement is true? [NCERT Exemplar]

Moderate

A

Buoyancy will be less in water at 0° C than that in water at 4° C.
B

Buoyancy will be more in water at 0° C than that in water at 4° C.
C

Buoyancy in water at 0° C will be same as that in water at 4° C.
D

Buoyancy may be more or less in water at 4° C depending on the radius of the sphere.

Solution

Let volume of the sphere be V and $ρ$ be its density, then we can write buoyant force as
F = V $ρ$ g (g = acceleration due to gravity)
$\Rightarrow$ $F \propto ρ$ ( $∵$ V and g both are constants)
$\Rightarrow$ $\frac{F_{4 ° C}}{F_{0 ° C}} = \frac{ρ_{4 ° C}}{ρ_{0 ° C}} > 1$ $(∵ ρ_{4^{\circ} C} > ρ_{0^{\circ} C})$
Hence, buoyancy will be less in water at 0° C than that in water at 4° C.

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