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 area of each chamber. A = 1 1 = 1 m ^2 . Distance between plates is d = 2 m . At t = 0 , the left chamber is completely filled with liquid ( _r = 15 ) and right chamber is empty ( _r = 1 ). Initial capacitance C(0) = C₁ + C₂ = 15 ₀ A d + ₀ A d = 15 ₀ (1) 2 + ₀ (1) 2 = 8 ₀ . Let y₁ and y₂ be the liquid levels in the left and right chambers at time t . By conservation of volume, y₁ + y₂ = 2 m . Let h = y₁ - y₂ . The velocity of efflux from the left chamber is v = 2gh . Rate of flow Q = -A dy₁ dt = a 2gh