Ncert Exercises & Solutions

An aluminium sphere is dipped into the water. Which of the following is true?

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

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

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

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

(1) Hint: The buoyancy of water depends on the density of the water.

Step 1: Find the buoyant force of water.

Let the volume of the sphere is V and

ρ

is its density, then we can write,

Buoyant force, F=V

ρ

g (g=acceleration due to gravity)

\Rightarrow F \propto ρ

(

∵

V and g are almost constant)

Step 2: Compare the buoyant force of water at different densities.

\Rightarrow \frac{F_{4 ° C}}{F_{0 ° C}} = \frac{ρ_{4 ° C}}{ρ_{0 ° C}} > 1 (∵ ρ_{4 ° C} > ρ_{0 ° C})

\Rightarrow F_{4 ° C} > F_{0 ° C}

Hence, the buoyancy will be less in water at 0

°

C than that in water at 4

°