Question

A boy has $60$ $kg$ weight. 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 $1000$ $kg/m^3$)

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

Answer 1

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

From Archimedes' principle

Weight of $(boy+log)=$ weight of water displaced

$(60+V\times 0.6\times {10}^3)g=V\times {10}^{3}g$

$\Rightarrow 0.4\times {10}^{3}V=60$

$\Rightarrow V=\frac{60}{0.4\times {10}^3}=\frac{60}{400}=\frac{3}{20}{m}^3$