Question

An ice block having two similar metallic pieces is floating in water in a vessel as shown in figure. After sometime the ice melts completely then

• A. The water level rises in the vessel
• B. The water level falls in the vessel
• C. The water level does not change in vessel
• D. The water level may rise or fall depending upon the ratio of masses of ice and metallic pieces.

Answer 1

Answer: (B)

Initially $f _{ B }= mg \,\,\,m _{ p }=$ mass of metal
$V _{ D _{ i }} \rho wg \left(2 n _{ p }+ m _{ i }\right)_{ g } m _{ i }=$ mass of ice $V _{ D _{ i }}=\frac{2 m _{ p }}{\rho_{ w }}+\frac{ m _{ i }}{\rho_{ w }} \,\rho_{ w }=$ density of water
$\rho_{ p }=$ density of metal piece
When ice metals completely, the metal pieces will sink down to the bottom.
Final displace volume $- V _{ D }=\frac{2 m _{ p }}{\rho_{ p }}+\frac{ m _{ i }}{\rho_{ w }}$
$\because V _{ D }< V _{ D _{ i }} \Rightarrow $ level falls