Question

An ice cube of edge length $20cm$ is floating in a tank of base area $2500$ $c{m}^2$ filled with water to $22cm$ height . The displacement of centre of mass of whole system (in cm), when ice cube melts completely will be
$({\rho }_{ice}=900kg/m^3,{\rho }_{\omega }=1000kg/m^3,g=10m/s^2)$

• A. $1$
• B. $1.5$
• C. $1.32$
• D. $1.44$

Answer 1

The correct option is A $1$

$Y_{CM}=\frac{M_1{Y}_1+M_2{Y}_2}{M_1+M_2}$

Let the Initial center of mass be $Y_{Initial}$ and the final center of Mass be $Y_{Final}$
The total mass of the system ( M ) and mass of ice (m) remains same .
Also , The mass , as well as the center of mass of the water present initially in the tank does not change .

Rise in water due to the melting of ice $=\frac{900\times 8\times {10}^{-3}}{1000\times 2500\times {10}^{-4}}=2.88cm$

Hence , displacement in center of mass is given by

$-Y_{final}+Y_{initial}=\frac{m(10-1.44)}{M}=\frac{1000\times 2500\times 2.88\times 8.56}{1000\times 2500\times (22+2.88)}=1cm$