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