Question

A fire wood board floats in fresh water with $60\%$ of its volume under water. The density of the wood in $g/c{m}^3$ is

• A. $0.4$
• B. $0.5$
• C. $0.6$
• D. $<0.4$

Answer 1

The correct option is C $0.6$

The total set Weight is equal to the buoyant force .

$p=$ density of substance, $p^{\prime }=$ density of water

We know, Buoyant force = mass of water displaced and $p=$ mass/volume.

$p\times$total volume$\times g=$Volume under water$\times p^{\prime }\times g$

Let $v=$ Total volume, $V^{\prime }=$ Volume under water

Therefore, $p=v^{\prime }/V\times$density of water which was assumed to be $1g/{cm}^3$.

That is, $p=0.6$

Hence, density of the water is equal to fraction of substance under water. That is, $0.6$