**Question:**

(a) A cube of side $5 \mathrm{~cm}$ is immersed in water and then in saturated salt solution. In which case will it experience a greater buoyant force.

If each side of the cube is reduced to $4 \mathrm{~cm}$ and then immersed in water, what will be the effect on the buoyant force experienced by the cubeas compared to the first case for water. Give reason for each case. (CBSE 2012)

(b) A ball weighing $4 \mathrm{~kg}$ of density $4000 \mathrm{~kg} \mathrm{~m}^{-3}$ is completely immersed in water of density $10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$. Find the force of buoyancy on it. (Given $g=10 \mathrm{~ms}^{-2}$.)

**Solution:**

(a) Buoyant force $=V \rho g$. Since, density $(\rho)$ of saturated salt solution is more than that of water. So, the cube will experience greater buoyant force in saturated salt solution. When size of cube is reduced, its volume (V) also reduces. Hence, it will experience less buoyant force then in first case.

(b) Buoyant force $=\mathrm{V} \rho \mathrm{g}=\left(\frac{\text { mass of ball }}{\text { density of ball }}\right) \times$ density of water $\times g=\frac{4}{4000} \times 10^{3} \times 10=10 \mathrm{~N}$.