# Calendar: 1875-1876 Page 598

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5 ENGINEERING AND APPLIED SCIENCES celeration at Ascension also how many heats does the pendulum gain in day at Konigsberg 11 solid pulley of given radius turns freely about hori- zontal axis fine thread is wrapped round it to the end of which weight equal to the weight of the pulley is attached the weight of the string and of the passive resistance being neglected find the angular velocity acquired when the pulley has made one revolution from rest FIRST YEAR Explain clearly how forces may be properly represented by straight lines What advantage is obtained by so representing them Define the resultant of any number of forces If system of forces be in equilibrium prove that each of these forces is equal to the resultant of all the rest and acts in direction directly opposite to the direction of that resultant rod feet long has weight of lbs at one end lbs at 30 inches from the end lbs at 54 inches 10 lbs at 80 inches and 16 lbs at the other end find at what point the rod must be supported Whnt is lever When two parallel forces act on straight lever find the conditions which must be satisfied in order that the lever may remain in equilibrium What is the centre of gravity of body right-angled isosceles triangle is cut out of circle its angular points being on the circle Find tbe position of the centre of gravity of the remainder If three moveable pulleys the weights of which are ozs ozs and 16 ozs be arranged as in the first system in the most advantageous manner what is the least forie that will raise weight of 104 lbs Find also the force required when the pulleys are arranged in the least advantageous manner Two inclined planes of the same height one of which is feet long and the other 10 are placed so as to slope in opposite directions and so that their summits coincide weight of

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