91Ó°ÊÓ

The density of wooden block is \(\rho = 0.60 \times {10^3}\;{\rm{kg/}}{{\rm{m}}^3}\).

The mass of the block is \(m = 0.40\;{\rm{kg}}\).

When a copper weight is placed on the top of a floating wooden block inside a container full of water, the buoyant force acting on the block will be equivalent to the total weight of the copper as well as wood.

The relation from buoyant forceis given by,

\(\begin{array}{c}{F_{\rm{g}}} = {F_{\rm{0}}}\\\left( {m + {m_{\rm{c}}}} \right)g = {V_{\rm{w}}}{\rho _{\rm{w}}}g\\\left( {m + {m_{\rm{c}}}} \right) = \left( {\frac{m}{\rho }{\rho _{\rm{w}}}} \right)\end{array}\)

Here, \({F_{\rm{g}}}\) is the force due to gravity, \({F_{\rm{0}}}\) is the buoyant force, \({V_{\rm{w}}}\) is the volume of the wood, \({\rho _{\rm{w}}}\) is the density of water, \(g\) is the gravitational acceleration and \({m_{\rm{c}}}\) is the mass of the copper.

On plugging the values in the above relation.

\(\begin{array}{c}\left( {0.40\;{\rm{kg}} + {m_{\rm{c}}}} \right) = \left( {\frac{{0.40\;{\rm{kg}}}}{{0.60 \times {{10}^3}\;{\rm{kg/}}{{\rm{m}}^3}}}\left( {1000\;{\rm{kg/}}{{\rm{m}}^3}} \right)} \right)\\{m_{\rm{c}}} = 0.26\;{\rm{kg}}\end{array}\)

Thus, the mass of the copper is \(0.26\;{\rm{kg}}\).