Question

Four rods side 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 figure. The rate at which vertex B is nearing the X-axis at the moment the rhombus is in the form of a square is

Answer 1

Answer:

The answer will be v/2

Explanation:

According to the problem the rods are placed in with their respective length in the stated structure. The vertex A is said to be in rigid position and Vertex C is moving along with X axis.

Now let the velocity components of vertex B is Vy and Vx

Now the rod B is moving towards x axis therefore the angle of moving is 45 degree as it is square

Therefore along the length velocity, vcos45 = Vxcos45+Vycos45

                                                            = v/√2 = Vx/√2 +Vy/√2

Now the rod B is moving towards x axis therefore the angle of moving is 45 degree as it is square

therefore Vxcos45 -Vycos45 = 0 [ as length is not increasing]

Therefore Vx= Vy

Now substitute the values

v/√2 = Vy/√2 +Vy/√2

Therefore Vy = v/2