The two indentical rectangular stell frames with the dimensions shown are farbricted from a bar of the same material and are hinged. Rectangular at the midpoints `A` and `B` of their side `(3mxx1m)`. If the frame is resting in the position shown on a horizontal surface with negligible friction, determine the velocity `v` with which each of the upper ends of the frame hits the horizontal surface if the cord `D` is cut. (Take the value of dimensions shown in the figure `c=1 m`, `b=3//2 m` and `theta=174^(@)` i.e., `sin"(theta)/(2)=(3)/(5)` and `cos"(theta)/(2)=(4)/(5)` & `g=10 m//s^(2)`)

Options

A. `5 m//s`
B. `8 m//s`
C. `3 m//s`
D. `4 m//s`

Explanation

Let the mass per unit length of the bar be `lambda(kg//m)`
As the frames come down, the point `B` moves vertically downwards and `PP'` remain in contact with the ground. In the final state (when `PQ`, `P'Q'` just become horizontal), the velocitites of `P` (and `P'`) is zero. The vertical component was already zero, the horizontal component also becomes zero. The motion of `PQ` is essentially rotation about `P` at that instant. Conservation of mechanical energy gives (for `PQ`) :

`(2lambda+6lambda)g(3)/(2)cos37^(@)=(1)/(2)((1)/(3)*6lambda*3^(2)+lambda*3^(2))omega^(2)`
and `v_(Q)=omega*PQ=omegaxx3=8m//s`