Question

A small lead shot is embedded in a big lump of ice floating in a jar of water. The level of water in the jar is noted. When all the ice melts down, the level of water in the jar would:

• A. be raised
• B. go down
• C. remain unchanged
• D. None of these

Answer 1

Answer: (B)

go down

Let $f$ be the fraction of ice inside water when floating on it in equilibrium and $m$ be the mass of the lead shot.

$⟹fV{\rho }_{water}g=mg+V{\rho }_{ice}g$

$⟹f=\frac{mg}{V{\rho }_{water}g}+\frac{{\rho }_{ice}}{{\rho }_{water}}>\frac{{\rho }_{ice}}{{\rho }_{water}}$

Volume of water formed by melting of ice=$\frac{V{\rho }_{ice}}{{\rho }_{water}}<fV=$volume inside water before melting

Hence the water level has gone down.