Question

Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.

Answer 1

Given:
Mass of wood, m_w = 200 g
Specific gravity of wood, ${\rho }_W$ = 0.8 gm/cc
Specific gravity of lead, ${\rho }_{PB}$= 11.3 gm/cc
$$\begin{gathered} \mathrm{We}\mathrm{know}: \\ Mg=w \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ (m_w+m_{pb})g=V_w\times \rho \times g[\mathrm{\rho }=\mathrm{Density}\mathrm{of}\mathrm{water}] \\ \Rightarrow 200+m_{pb}=\frac{200}{0.8}\times 1 \\ \Rightarrow m_{pb}=250-200=50\mathrm{gm} \end{gathered}$$