Question

A cubical block of copper is immersed completely in water. Each edge of the block is $1\text{cm}$ in length. Find the buoyant force acting on the cube. The density of water $=1,000{\text{kg/m}}^3$.

• A. $9.8\times {10}^{-2}\text{N}$
• B. $9.8\times {10}^{-4}\text{N}$
• C. $9.8\times {10}^{-5}\text{N}$
• D. $9.8\times {10}^{-3}\text{N}$

Answer 1

The correct option is D $9.8\times {10}^{-3}\text{N}$

The volume of the blocks is $(1\text{cm}{)}^3={10}^{-6}{\text{m}}^3$.
The block displaces this much volume of water when immersed completely in water.
The mass of this water is
$M=\text{(volume)}\times \text{(density)}=\left({10}^{-6}{\text{m}}^3\right)\times \left(1000{\text{kg/m}}^3\right)={10}^{-3}\text{kg}.$
Weight of this water = $Mg=\left({10}^{-3}\text{kg}\right)\times \left(9.8{\text{m/s}}^2\right)=9.8\times {10}^{-3}\text{N}.$
Thus, the buoyant force on the cube is $9.8\times {10}^{-3}\text{N}.$