A rod of length $$1$$ $$m$$ is sliding in a corner as shown in Fig.$$2.7.$$ At an instant when the rod makes an angle of $$60$$ degrees with the horizontal plane, the velocity of point $$A$$ on the rod is $$1$$ $$m/s$$. The angular velocity of the rod at this instant is

Fig. shows a quick return mechanism. The crank $$OA$$ rotates clockwise uniformly. $$OA=2$$ cm, $$O{O^1} = 4$$ cm. The ratio of time for forward motion to that for return motion is

The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in the figure is:

Instantaneous center of a body rolling with sliding on a stationary curved surface lies