# Calendar: 1899-1900 Page 764

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ο CX11 FACULTY OF SCIENCE 11 The space enclosed between two spherical surfaces which touch internally is completely filled with water and the Centre of Gravity of the water lies midway between the centre of the inner sphere and the surface of the outer Find the radius of the inner sphere that of the outer being 10 in 12 float hollow throughout consists of right circular cylinder length Λ with hemisphere at one end and cone at the other their bases being equal and their axes in the same straight line they are made of the same material and their cubical contents are the same Find the distance of the Centre of Gravity of the whole from the vertex of the cone 13 Explain the terms Moment of Inertia7 and 4Radius of Gyration Prove that if the radius of gyration of body about any axis be given the radius of gyration about parallel axis can be found if the distances of the axes from the Centre of Gravity be known Find the radius of gyration of right circular cylindei about tangent line to the circumference of the base JHatijemattcs II algebra anli GEttgonametrg Candidates for the Preliminary Certificate and for the Special Matriculation Certificate are expected to answer of the ques- tions on Algebra and of the questions on Trigonometry Queen's Scholars year are expected to answer questions 1-5 II III years 5-8 Candidates for the London University Intermediate Exam- ination are expected to answer questions 5-14 Candidates for College Certificates of Distinction and Merit after they have answered' the questions expected from them may answer any of the subsequent questions Prove that a2 b2 402 a2 b2 U2 and that if and are integers and a2 b2 is prime to each of these expressions is multiple of 576 Solve the equation χ -3 χ-1 χ--2 χ-3 and if χ χ 2y 3z 2y 32 2y 3z

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