Question

A lump of ice is floating in water in a cylindrical vessel of bottom area S. The ice piece is tied from the bottom of the vessel with the help of a thread as shown in the figure. When the whole ice melts, the water level in the vessel drops by $\Delta h$. Find the tensile force in the thread before melting of the ice. Acceleration due to gravity is g.

Answer 1

T = $\Delta h S \rho_w g$

Answer 2

The tensile force in the thread is equal to the product of the drop in water level ($\Delta h$), the base area of the vessel ($S$), the density of water ($\rho_w$), and the acceleration due to gravity ($g$). This arises because the tension causes the ice to displace an additional volume of water compared to the volume of water it forms upon melting. This excess displaced volume, when spread over the area $S$, accounts for the observed drop in water level $\Delta h$.