Four rods of side length `l` have been hinged to form a rhombus. Vertex `A` is fixed to a rigid support, vertex `C` is being moved along the `x`-axis with 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 squarem is

Options

A. `V/4`
B. `V/(sqrt(2))`
C. `V/2`
D. `(V^(2))/g`

Answer

C

Explanation

Let velocity components of point `B` are `upsilon_(x)` and `upsilon_(y)`. Along the length of rod, velocity of each point must be same (rigid body constraint)
`(upsilon_(x))/(sqrt(2))+(upsilon_(y))/(sqrt(2))=V/(sqrt(2))` (along rod `2`)
`(upsilon_(x))/(sqrt(2))-(upsilon_(y))/(sqrt(2))=0` (along rod `1`)
`upsilon_(x)=upsilon_(y)=V/2`