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

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately

The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of friction (µ) at the gripping surface is $$0.1$$ $$XX$$ is the line of action of the input force and $$Y - Y$$ is the line of application of gripping force. If the pin joint is assumed to be frictionless, the magnitude of force $$F$$ required to hold the weight is