A circular object of radius r rolls without $$V$$ slipping on a horizontal level floor with the center having velocity $$V.$$ The velocity at the point of contact between the object and the floor is

A rigid link PQ is 2 m long and oriented at 20^o to the horizontal as shown in the figure. The magnitude and direction of velocity V_Q, and the direction of velocity V_P are given. The magnitude of V_P(in m/s) at this instant is

A slider-crank mechanism with crank radius $$60$$mm and connecting rod length $$240$$mm is shown in figure. The crank is rotating with a uniform angular speed of $$10$$ rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is ____________.

An offset slider - crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______