A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction

If the quick return ratio is $$1:2$$, then the length of the crank in mm is

The input link Q₂P of a four bar linkage is rotated at $$2$$ rad/s counter clockwise direction as shown below. The angular velocity of the coupler PQ in rad/s, at an instant when $$\angle {O_4}{O_2}P = {180^ \circ },$$ is

A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction

The angular speed of PQ in rev/s when the block R attains maximum speed during forward stroke (stroke with slower speed) is

Match the items in column $$I$$ and $$II$$

List $$I$$
$$P.$$ Higher kinematic pair
$$Q.$$ Lower kinematic pair
$$R.$$ Quick return mechanism
$$S.$$ Mobility of a linkage

List $$II$$
$$1.$$ Grubler's equation
$$2.$$ Line contact
$$3.$$ Euler's equation
$$4.$$ planar
$$5.$$ Shaper
$$6.$$ Surface contact