Physics Question from JEE Main 2025 · 8 April, Shift 2

A cube having a side of $10 \, \text{cm}$ with unknown mass and $200 \, \text{gm}$ mass were hung at two ends of an uniform rigid rod of $27 \, \text{cm}$ long. The rod along with masses was placed on a wedge keeping the distance between wedge point and $200 \, \text{gm}$ weight as $25 \, \text{cm}$. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of the unknown mass is more than that of the water, the mass did not absorb water and water density is $1 \, \text{gm/cm}^3$.) The unknown mass is _____ $\text{kg}$.