Question

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

Answer 1

Step 1: Given Data

Mass of the ball $m=4kg$

The density of the ball ${\rho }_b=4000kg{m}^{-3}$

The density of water ${\rho }_w={10}^{3}kg{m}^{-3}$

Acceleration due to gravity $g=10m{s}^{-2}$

Step 2: Volume of the Ball

We know that if $V$ is the volume of the ball,

${\rho }_b=\frac{m}{V}$

$\Rightarrow V=\frac{m}{{\rho }_b}$

$\Rightarrow V=\frac{4kg}{4000kg{m}^{-3}}$

$\Rightarrow V=\frac{1}{1000}{m}^3$

Step 3: Calculate the Buoyant Force

We know that the buoyant force is given as

$b=V{\rho }_{w}g$

$\Rightarrow b=\frac{1}{1000}{m}^3\times {10}^{3}kg{m}^{-3}\times 10m{s}^{-2}$

$\Rightarrow b=10N$

Hence, the force of buoyancy on the ball is $10N$.