Calendar: 1881-1882 Page 663

664 APPLIED SCIENCES With single fixed and single movable pulley find the greatest weight which power of 100 lbs is capable of supporting when the radius of the pulley is inches the radius of the axis inch and the coefficient of friction An embankment of brickwork in the form of right- angled triangle sustains the pressure of water on its vertical face its base is feet and its height 12 feet find the greatest height of water so that it may not be overthrown What is meant by moment of inertia Find the moment of inertia of cylinder about its axis and deduce the moment of inertia of circular disc about diameter FIRST YEAR An express train 60 yards long moving at the rate of 50 miles an hour meets slow train 120 yards long moving at the rate of 20 miles an hour Find how long man in the express train takes to pass the slow train and how long the express train takes in completely passing the slow train ball is allowed to fall to the ground from height of 64 feet and at the same instant another ball is thrown upwards with just sufficient velocity to carry it to the height from which the first falls find when the balls will pass each other State the Third Law of Motion Show that if the lighter of two weights fastened to the ends of string passing over pulley moving without friction be of the heavier the velocity gained in any time is £ of that of falling body in the same time Find also the tension of the string if the lighter weight be equal to lb wheel and axle is used to raise bucket from well the radius of the wheel is 20 inches and while the wheel makes three revolutions the bucket which weighs 30 lbs rises one foot find the smallest force which can turn the wheel Explain how it is that in drawing water from deep well the difficulty increases slightly as the bucket ascends man attempts to raise himself by an arrangement of