Calendar: 1899-1900 Page 780

cxxviii FACULTY OF SCIENCE J&edj antes SECOND AND THIRD YEARS An engine is employed to wind up chain each foot of which has mass of lbs the chain is suspended from the top and reaches to the bottom of shaft whose depth is 20 fathoms divide it into two parts so that the work done in the winding up of each part is the same ladder 16 feet long with its centre of gravity ft from the bottom stands on horizontal plane with the top resting against vertical wall of the same material coefficient of friction 35 find the position in which it is on the point of slipping piece of wood inches square is cut out of the corner of another piece of wood inches square find the position of the centre of gravity of the remainder cylinder of iron rests on an inclined plane of oak it is on the point of sliding down and of overturning it is inches in radius and its height is feet find the coefficient of friction between iron and oak Show that the direction of the smallest force which will draw body down an inclined plane makes an angle with the plane equal to the limiting angle of friction An inclined plane is being driven in between fixed block and block Ε which moves between guides find the relation between the power at the back of the inclined plane and the resistance offered by E9 taking into account only the friction on the face AG Hence find the relation between the power and the weight on rough screw An equilateral triangle revolves round an axis in its plane and parallel to its base the base is feet long and the