Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( M₁ and M₂ ) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area 10 cm ^2 near its bottom edge. Initially the

Step-by-step solution

Let A be the cross-sectional area of each chamber and a be the cross-sectional area of the hole. From the given dimensions, the area of each chamber is A = 1 m 1 m = 1 m ^2 . The area of the hole is a = 10 cm ^2 = 10 10⁻⁴ m ^2 . Let h₁ and h₂ be the heights of the liquid in the left and right chambers at time t , respectively. By conservation of volume, A h₁ + A h₂ = A H , where H = 2 m is the initial height of the liquid in the left chamber. h₁ + h₂ = 2 The velocity of efflux through the hole is given by Torricell