Calendar: 1861-1862 Page 504

APPLIED SCIENCES 505 The questions upon these subjects were the same as those set For the Middle Mathematical Scholarship in the Department of General Literature and Science IV -Jlatural SPosiopiig State completely the conditions of equilibrium in the fol- lowing cases two forces β three parallel forces any three forces δ any number of forces acting on body in one plane rectangular board whose dimensions are 90 inches horizontal and 60 inches vertical has portion cut off from one corner in the form of triangle extending 60 inches along the horizontal side 30 inches along the vertical side Find the distance of the centre of gravity of the remainder from the other horizontal and vertical sides Two uniform beams 40 and 30 feet long and weighing res- pectively 400 lbs and 300 lbs are joined at their extremities Their other extremities are connected by rope 50 feet long and rest on the tops of two walls of equal height find the pres- sure on each wall and β the tension of the rope Find the force requisite to move weight up rough inclined plane the force being applied horizontally Ex Length of plane feet height feet base feet co- efficient of friction μ 96 lbs Find the work done by the force in raising to the top of the plane Two bodies Ρ and are connected by string and revolve in circles Show that the point about which they revolve must be their centre of gravity and find the tension of the string its length being and the time of revolution body is projected with velocity of 000 feet per second at an angle to the horizon so that sin and cos Find the position of the body after 40 second and the range- and time of flight on horizontal plane Define angular velocity moment of inertia radius of gyra- tion and centre of oscillation Find the moment of inertia of straight uniform rod about one end and find the length of pendulum that would vibrate in the same time