Question

Four rods of equal length L are joined by four pins A,B,C `&` D as shown in the figure. Rods are free to rotated about pins. Pin A is given velocity `v_(0)` and pin C is given `3v_(0)` as shown

The angular velocity of rod BC is
A. `(2v_(0))/(L)`
B. `(2v_(0))/(L) sin theta`
C. `(2v_(0))/(L sin theta)`
D. `(2v_(0))/(L)costheta`

Answer 1

`v sin theta+2v_(0) cos theta=4v_(0) cos theta`
`rArr v=2v_(0) cot theta`
`therefore v_(B)=2v_(0) cosec theta`

`omega=(2v_(0)sin theta+v cos theta)/(L)=(2v_(0))/(L sin theta)`