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Four rods each of length l have been hinged to form a rhombus. Vertex A is fixed to rigid support, vertex C is being moved along the x -axis with a constant velocity v as shown in the figure. The rate at which vertex B is approaching the x -axis at the moment the rhombus is in the form of a square is -

Options

  1. Av 4
  2. Bv 3
  3. Cv 2
  4. Dv 2

Correct answer

C. v 2

Step-by-step solution

Let A C = x and B E = y Then, B E 2 + A E 2 = l 2 or y 2 + x 2 2 = l 2 ∴ 2 y d y d t + x 2 . d x d t = 0 ∴ - d y d t = 1 2 x 2 y . d x d t x = 2 y , when the rhombus is a square. Hence, v B = 1 2 v c = v 2

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