GATE ME 2022 Set 2 — Question 62
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Fluid Mechanics → Fluid Properties & Statics → Buoyancy & Stability
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Question
A uniform wooden rod (specific gravity = , diameter = cm and length = m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = ) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod. Assume density of water = kg/m and . Radius of the ball is _______ cm (round off to 2 decimal places).
Correct answer
3.48 to 3.7
Solution
Let m be the length of the rod, m be its diameter, and be its specific gravity. Let be the radius of the lead ball and be its specific gravity. The rod is hinged at point A on the waterline. For static equilibrium, the sum of moments about hinge A must be zero.Forces acting on the system:
1.Weight of the rod (): , acting at from A.
2.Buoyancy force on the rod (): , acting at from A.
3.Weight of the ball (): , acting at from A.
4.Buoyancy force on the ball (): , acting at from A.
Taking moments about A:where is the angle of the rod with the horizontal. Dividing by :Rounding off to two decimal places, the radius of the ball is cm.Continue learning with Success Tracker
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