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

An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 10³ N/m. It is pre-compressed by 100mm from its free state. If it is used to eject mass of 100kg heald on it, the mass will move up through a distance of

A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balancing mass of 20 kg is attached as shown in fig.(b). The percentage increase in mass moment of inertia as a result of this addition is