Question #42438

A block of mass $m = 5 \text{ kg}$ and variable internal density (configured such that its center of mass is at its base to prevent toppling) rests on a fixed rough wedge of angle $\theta = 37^\circ$. The block is connected to a hanging mass $M = 4 \text{ kg}$ via a light inextensible string passing over a frictionless pulley at the top of the wedge, with the string parallel to the incline. The coefficient of static friction between the block and the wedge is $\mu = 0.5$. Initially, the system is in static equilibrium. Water of density $\rho_w = 1000 \text{ kg/m}^3$ slowly fills the container holding the wedge. Find the submerged volume of the block (in liters) at the exact moment it begins to slip up the incline. (Take $g = 10 \text{ m/s}^2$, $\sin 37^\circ = 0.6$, $\cos 37^\circ = 0.8$)