GATE 2021 CE (CE1) – Question 59
A horizontal cylinder has diameter 2 m, length 3 m and weight 25 kN. Water on its left reaches 1 m above its top; oil of specific gravity 0.8 on its right reaches the cylinder centre. Find |net vertical force|/|net horizontal force| to two decimals.
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Correct answer: .35 to .40
Explanation
Horizontal resultant is $9.81(3)(2)(2)-0.8(9.81)(3)(1)(0.5)=105.948$ kN. Upward vertical fluid force is the displaced left semicylinder plus right quarter-cylinder: $9.81(3)(\pi/2)+0.8(9.81)(3)(\pi/4)=64.7205$ kN. Subtract the 25 kN weight; the ratio is $39.7205/105.948=\mathbf{0.37}$.