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  Item Reference: KCLCAL-1863-1864-523

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GENERAL LITERATURE AND SCIENCE 523 projected parallel to the axis find the form of the curve which will be described 10 If Xand J"be the coordinates of the centre of gravity of the area PAp cut off from parabola by focal chord Ρ Sp inclined to the axis at an angle cot2 Τ 2a cot 11 Find the centre of gravity of the half of the lemniscata whose equation is r2 a2 cos 16 12 If the price of pure whisky be 16s per gallon and its specific gravity be 75 what should be the price of mixture of whisky and water the specific gravity of which is 13 weight will rest upon rough plane inclination but if the inclination be Θ force Ρ will be requisite acting parallel to the horizon find 14 Find the coordinates of the centre of pressure of plane area immersed in fluid 15 vertical floodgate has horizontal axis find its position when the gate is in vertical position If the gate turn on hinges in one side find where single force may act to maintain equi- librium and find that force 16 Β is vertical line Ρ curve in the same plane beam Ρ rests between them find the equation to Ρ that Ρ may rest in all positions 17 cone is placed on its base upon rough inclined plane the inclination of which is gradually increased find the condi- tions that it may just roll and slide at the same moment 18 rectangular plate ABCD hangs by cord at and is partly immersed in water the diagonal BD coinciding with the surface required the weight of the plate and the tension of the string II -$ure iHatijfmattci Expand in ascending powers of and find the co- ex efficient of χ
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