The number of degrees of freedom in a planner mechanism having $$n$$ links and $$j$$ simple hinge joints is

A rigid link $$PQ$$ is undergoing plane motion as shown in the figure ($${V_P}$$ and $${V_Q}$$ are non-zero). $${V_{QP}}$$ is the relative velocity of point $$Q$$ with respect to point $$P$$.

Which one of the following is TRUE?

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______

In the figure, link $$2$$ rotates with constant angular velocity $${{\omega _2}}$$. A slider link $$3$$ moves outwards with a constant relative velocity $${V_{Q/P,}}$$ where $$Q$$ is a point on slider $$3$$ and $$p$$ is a point on link $$2.$$ The magnitude and direction of Coriolis component of acceleration is given by