Calendar: 1873-1874 Page 616

616 THE SCHOOL If cos θ φ cos -f prove that sin2 sin 13 Express cos Θ in series of cosines of multiples of and express cos sin Θ in terms of cosines of multiples of β iHrrijjaiucS Explain what is meant by 'force Show that any force can be properly represented by straight line Define the resultant of two forces Enunciate the parallelogram of forces and assuming it for the direction prove it for the magnitude of the resultant If three forces balance each other prove that either they are parallel or they meet in point Three rods AB BC CA are jointed together so as to form triangle and the system lies on smooth horizontal table if tightened string connect the middle points of Β and AC find the directions of the actions at the three joints Define the centre of gravity of heavy body and find the centres of gravity of the area of triangle and of the two portions into which it is divided by straight line bisecting two of its sides If heavy body be suspended from point prove that it can otdy rest with its centre of gravity in the vertical line through the point triangular plate of iron of uniform thickness rests inside smooth hemispherical bowl prove that the three pressures on the bowl are equal Find the ratio of the power to the weight- 1st On smooth inclined plane 2nd On smooth screw 3rd In the system of pulleys in which each hangs by separate string State the laws of statical friction and find the least force by which heavy body lying on rough horizontal plane can be moved