Calendar: 1859-1860 Page 451

452 APPLIED SCIENCES When rigid body swings about fixed axis under the action of gravity determine the motion Prove that the centres of oscillation and suspension are con- vertible sphere revolving about tangent line which is horizontal makes complete revolutions find the greatest pressure upon the axis Enunciate the principle of vis viva and apply it to find the work stored up in rod feet long weighing 50 lbs and revolving about vertical axis so as to make revolutions in second Find the time in which sphere will roll down given in- clined plane circular plate of one foot radius weighs lbs weight of 10 lbs is fastened to string wound round the circumference of the plate and descends by turning the plate Find the space described in five seconds -ffipUroStattci Find the centre of pressure of plane area immersed in fluid Ex semicircle whose base is in the surface hemisphere is partly filled with fluid whose density varies as the depth When the surface of the fluid bisects vertical radius the ratio of the whole pressure on the cup to the weight of the fluid will be 16 Find the centre of pressure of right-angled triangle whose hypothenuse is in the surface of the fluid Define the metacentre of floating body and show how to find it If hemisphere floats in fluid with its base downwards prove that the distances of the metacentre and centre of gravity from the base are in the ratio of the densities of the solid and fluid