The average pressure an object exerts on a surface is given by the formula:

Pressure = Force / Area

The force exerted by the object is its weight, which is given by:

Weight = Mass * g

The mass of the object can be found by multiplying its volume by its density. For a hemisphere, the volume is half that of a sphere, so:

Volume = 1/2 * 4/3 * π * r^3 = 2/3 * π * r^3

So, the mass is:

Mass = Volume * Density = 2/3 * π * r^3 * ρ

Substituting this into the formula for weight gives:

Weight = 2/3 * π * r^3 * ρ * g

The area over which this force is distributed is the area of the flat surface of the hemisphere, which is a circle of radius r. So:

Area = π * r^2

Substituting the expressions for weight and area into the formula for pressure gives:

Pressure = (2/3 * π * r^3 * ρ * g) / (π * r^2) = 2/3 * r * ρ * g

So, the average pressure the object exerts on the table is 2/3 * r * ρ * g, which is closest to option D: 32ρ rg.

Question

The average pressure an object exerts on a surface is given by the formula:

Pressure = Force / Area

The force exerted by the object is its weight, which is given by:

Weight = Mass * g

The mass of the object can be found by multiplying its volume by its density. For a hemisphere, the volume is half that of a sphere, so:

Volume = 1/2 * 4/3 * π * r^3 = 2/3 * π * r^3

So, the mass is:

Mass = Volume * Density = 2/3 * π * r^3 * ρ

Substituting this into the formula for weight gives:

Weight = 2/3 * π * r^3 * ρ * g

The area over which this force is distributed is the area of the flat surface of the hemisphere, which is a circle of radius r. So:

Area = π * r^2

Substituting the expressions for weight and area into the formula for pressure gives:

Pressure = (2/3 * π * r^3 * ρ * g) / (π * r^2) = 2/3 * r * ρ * g

So, the average pressure the object exerts on the table is 2/3 * r * ρ * g, which is closest to option D: 32ρ rg.

Knowee AI · Accepted Answer