Calendar: 1883-1884 Page 626
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622 GENERAL LITERATURE AND SCIENCE 10 Find the volume generated by the revolution of about the initial line -f- cos Θ Find also the centre of gravity of this volume 11 Prove that when string is stretched over rough curve the tensions at the ends may be in the ratio βμφ where φ is the angle between their directions and μ the coefficient of friction Obtain the corresponding formula when the string is heavy and the curve circle in vertical plane Obtain also differential equation to determine the tension when the string is extensible 12 Integrate the differential equations dx3 ax by ax βν -f dl dx cosx sec χ 9secJ χΔ χ sec2V sec2 ד ax xyly px VpV b' where ρ siu2x isin 2a Ρ2 dy ן dx Division II XIV fUgtbra an& Crtgononutrj Simplify 3x 3y 3y 3x -z z-x z- י
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