Question

A boy of mass $60\text{kg}$. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$, what is the minimum volume of wooden log?
(density of river water is $1000{\text{kg/m}}^3$)

• A. $0.66{\text{m}}^3$
• B. $150{\text{m}}^3$
• C. $\frac{3}{1}{\text{m}}^3$
• D. $\frac{3}{20}{\text{m}}^3$

Answer 1

The correct option is D $\frac{3}{20}{\text{m}}^3$

Archimedes principle states that
weight of body displaced by liquid = upthrust.
By balancing forces
$60\times g+V\times 0.6\times {10}^3\text{g}=V\times 1000\text{g}$
$60+600\text{V}=1000\text{V}$
$60=400\text{V}$
$V=\frac{60}{400}=\frac{3}{20}{\text{m}}^3$
Where, $V$ is the volume of wooden log.