A block of ice in which a piece of stone is embedded is floating on water contained in a beaker. When all the ice melts the level of water in the beaker

Explanation

Let `m_(1)` be the mass of ice and `m_(2)` be the mass of stone. If `rho` is the density of water, then volume of water displaced by piece of ice is,
`V=((m_(1)+m_(2))/(rho)) = (m_1)/(rho) + (m_2)/(rho)`. When the ice melts, the additional volume of water obtained is `m_(1)//rho`. The stone sinks in water, it displaces the volume of water equal to its own volume `=(m_2)/(rho_s)` where `rho_(s)` is the density of stone . Thus the total volume of additional water is,
`V' = (m_1)/(rho) + (m_2)/(rho_s)`
Since, `rho_(s) gt rho or 1/(rho_s) lt 1/(rho)` therefore, `V' lt V`.
Therefore, level of water in a beaker decreases.