What happens to water level?

When the ice is floating,

$d_{water} v_{displaced} g = (M_{ice} + m_{lead} )g$

Therefore, $v_{displaced} = \frac{(M_{ice} + m_{lead} )}{d_{water}}$

When all the ice melts, it gets converted into water so volume displaced by it will be same as before. But, since the lead ball sinks in water, using Archimedes priciple, $V_{displaced} = \frac{m_{lead}}{d_{lead}}$

Now, the total volume displaced is

$V_{displaced} = \frac{M_{ice}}{d_{water}} + \frac{m_{lead}}{d_{lead}}$

Since, $d_{lead} > d_{water}$

$\textbf{The final volume displaced is less than initial volume displaced.}$

$So, water level falls!$

Actually the answer is "Insufficient Information," for we're not given that the ball doesn't disappear by the time the ice cube decides to melt.

But of course everyone assumes that Newtonian mechanics will rule all the time, and that's good enough for a commonthinker anyway.

dont use Archimedes principle use the law of flotation Let the mass of the lead shot be m then mass of water displaced is also m (first law of flotation). volume of water displaced v1 =mc.c (density of water 1g/c.c). When ice melts lead ball will sink. Then volume of water displaced= volume of lead shot v2 =(m/d )c.c, where d is the density of lead since d is grater than 1 v2 is less than v1 so level will fall

That's too easy , the answer is that the water level will decreases.