Question

On a large tray of mass M, an ice cube of mass m, edge L is kept. If the ice melts completely, the center of mass of the system comes down by:

• A. $\frac{mL}{2(M+m)}$
• B. $\frac{(M-m)L}{2(M+m)}$
• C. $\frac{(M+2m)L}{2(M+m)}$
• D. $\frac{2ML}{2(M+m)}$

Answer 1

The correct option is A $\frac{mL}{2(M+m)}$

It is a large tray,so when ice melts the level of water is negligible.
Shift in COM is basically the level of COM before melting
$ycm$ before melting
$=\frac{m\times \frac{L}{2}}{(m+m)}$
$\frac{mL}{2(m+m)}$