An ice block with a piece of lead embedded in it floats in water. If the ice melts the water level

An ice block with a piece of lead embedded in it floats in water. If the ice melts the water level 

(1) Rises 

(2) Falls 

(3) Remains same 

(4) Falls first and then rises

Answer: (2) If ρ1 is the density of the lead piece of volume v, the volume of water displaced by the ice block and the lead piece while floating is Vω = (V–v) ρ1 + v ρ1. When the ice melts, the lead piece sinks in water since ρ1 is greater than the density of water. The water produced by the melted ice has the volume (V-v) ρ1 and the volume displaced by the lead piece is v. So, the total volume of the water produced by ice and that displaced by the lead piece is V ω1 = (V–v) ρ1+ v ρ1< V ω. So, the water level goes down.