A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in the figure below. The coefficient of friction is $$\mu $$. If $$\mu < \tan \theta $$, then the time taken by the block to reach anorher point $$Q$$ on the inclined plane, where $$PQ=S,$$ is

If point A is in equilibrium under the action of the applied forces, the values of tensions and T _AB and T_AC are respectively.

An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight are connected by a chain that passes over a pulley. The pulley is coupled to a motor. It is desired that the elevator should have a maximum stopping time of t seconds from a peak speed $$V.$$ If the inertias of the pulley and the chain are neglected, the minimum power that the motor must have is

Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizontal force F. the minimum value of F for which slip occurs nbetween the two books is