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Wednesday, November 13, 2019

An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r and density ρ.


Question 33
An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r and density ρ.

The volume of a sphere is 4/3 π r3.

Which average pressure does the object exert on the table?
A 1/3 ρr2                      B 1/3 ρr2g                   C 2/3 ρr                      D 2/3 ρrg





Reference: Past Exam Paper – March 2019 Paper 12 Q14





Solution:
Answer: D.

The object is shaped as a hemisphere (half a sphere).


Pressure = Force / Area
Here, the force is the weight of the object and the area is the cross-sectional area of the object which is in contact with the table.


Volume of object = ½ × volume of sphere
Volume of object = ½ × 4/3 πr3 = 2/3 πr3

Density = mass / volume

Mass of object = ρV = 2/3 πρr3
Weight of object = mg = 2/3 πρr3g


The area in contact with the table has the shape of a circle of radius r.
Area = πr2


Pressure = Force (or weight) / Area
Pressure = (2/3 πρr3g) / (πr2)
Pressure = 2/3 ρrg

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