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.

Hint: According to Archimedes principle, the weight of water displaced is equal to the weight of the body floating in water. In this case the density of lead piece along with ice becomes less than water then it floats on water. But its volume is less than the water displaced by the lead piece due to its heavy weight.

Complete step by step solution:
We know that lead is a heavy metal its density is too greater than water. But along with ice its float due to balance of buoyancy force and gravitational force. On floating conditions, according to Archimedes principle, when ice and lead is floating on water then water displaced is equal to the mass of lead and floating ice. So, the water level has risen. But when ice melts and lead shrinks then its volume is less than the volume of water displaced during its floating due to density of lead is much higher than water and ice. So, its water level falls down.

Hence option (B) is correct.

Additional Information:
Buoyancy: When an object is placed in a fluid, the fluid exerts an upward force we call the buoyant force. The buoyant force comes from the pressure exerted on the object by the fluid. We know that when we go into depth the pressure increases as the depth increases, the pressure on the downward of an object is always larger than the force on the upward. Hence the net upward force is here. The buoyant force is present whether the object floats or sinks.

Note: We have to learn that the body submerges when the gravitational force is bigger than the buoyant force. It doesn’t depend on the object density directly. Yes, we can say that gravitational force depends on density or mass of the body. Buoyant force is always in upward direction.