Question

An ice cube containing a lead piece in it is floating in a vessel of water. As the ice melts, the water level will :

• A. Fall
• B. Rise
• C. Remains stationary
• D. None

Answer 1

The correct option is A Fall

If the ice cube initially contains the lead piece then as ${\rho }_{Pb}>{\sigma }_W$, it will sink when ice melts and so the water displaced by it will be equal to its own volume,
i.e., $V_2=\left(m/{\rho }_{Pb}\right)$ [as $\rho =m/V]$
So finally total volume occupied by water formed by melting of ice and lead piece.
$V_1+V_2=\frac{M}{{\sigma }_W}+\frac{m}{{\rho }_{Pb}}$
Now as ${\rho }_{Pb}>{\sigma }_W$, this volume will be lesser than initial by water displaced by the floating system (Eqn. 1); so the level of water is beaker will go down as the ice melts if the contains a sinking impurity.