A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coeficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s² . When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s² ) of the end P is _______

A circular object of radius r rolls without 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

Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$. The viscosity of water at $${25^ \circ }C$$ is $$0.001$$ $$kg/m.s.$$ The Reynolds number of the flow is ____________________