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 _______

In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is $$100$$ $$mm$$ and its tangential speed is $$10$$ $$m/s.$$ The dynamic viscosity of the lubricant is $$0.1$$ $$kg/m.s.$$ The frictional resisting force (in newton) per $$100$$ $$mm$$ length of the bearing is ______________.

For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stability will be