Calendar: 1887-1888 Page 670

674 GENERAL LITERATURE AND SCIENCE Find an integrating factor for and integrate Explain the application of the integral calculus to determine the centre of gravity of curve the equation of which is given in polar coordinates Find the centre of gravity of the portion from θ to 2a θ of the curve 14 costf An elastic string originally uniform hanging vertically with mass at the lower end the weight of which is equal to the modulus of elasticity is extended to three times its natural length prove that the mass of the string is twice the attached mass If the law of attraction be that of the inverse square of the distance prove that homogeneous shell attracts an external particle as if the mass of the shell were condensed at its centre 10 If particle move in parabola so that the resolved part of the velocity perpendicular to the axis is constant prove that it must be acted on by constant force parallel to the axis 11 mass moves under the action of force mP directed towards fixed centre prove that the differential equation of the path is where is constant depending upon the circumstances of projection Find the law of force to the origin under which cos Θ can be described 12 particle moves in the curve 40 sin φ so that its direction of motion rotates uniformly prove that it is acted on by force constant in magnitude