Water and mercury fill two cylindrical vessels to an identical height. Each vessel features a hole in the wall near its bottom. The velocities of the water and mercury emerging from these holes are v₁ and v₂ , respectively.

Step-by-step solution

According to Torricelli's law, the velocity of efflux of a liquid from a small hole at a depth h below the free surface is given by v = 2gh . This expression is independent of the density of the liquid. Since both vessels are filled to an identical height, the depth h is the same for both water and mercury. Therefore, the velocities of efflux are equal, which gives v₁ = v₂ .