A piece of ice floating in a vessel filled with water. As the ice piece melts, what happens to the water level if
(a) (i) ice melts and (ii) ice piece contains an air bubble
(b) ice piece contains (i) a lead piece and (ii) a cork piece.

Explanation

(i) Let `M` : mass of ice piece
For floatation : `Mg = rho_omega V_0 g rArr V_0 = (M)/(rho_(omega))`
`V_0` : volume of displaced water
when `M gm` ice melts, water formed will be `m gm` and it will occupy volume
`V = (M)/(rho_(omega))`
`V = V_0`, level of liquid remains same
(ii) Same answer, as weight of cavity is zero
(b) (i) `Mg + mg = rho_omega V_0 g`,
`m` : mass of lead piece
`V_0 = (M)/(rho_omega) + (m)/(rho_omega)`
when ice melts, lead will sink
New volume of water displaced, `V = (M)/(rho_omega) + (m)/(rho_l)`
`rho_l gt rho_omega i.e., V lt V_0`, level of liquid falls
(ii) `Mg + mg = rho_omega V_0 g`,
`m` : mass of cork
`V_0 = (M+ m)/(rho_omega)`
As cork piece floats, `V = (M)/(rho_omega) + (m)/(rho_omega)`
`V = V_0`, level of liquid remains same.