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Q.

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

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a

v2

b

v2

c

v3

d

v4

answer is B.

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Detailed Solution

Let AC=x and BE=y. Then  BE2+AE2=ℓ2⇒ y2+x22=ℓ2⇒ 2ydydt+x2dxdt=0⇒ −dydt=12x2ydxdtWhen the rhombus is a square, then x = 2y⇒vB=12vC=v2
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