Multiple choice

An object shaped as a hemisphere rests with its flat surface on a table. The object has radius r and density $\rho$. The volume of a sphere is $\dfrac{4}{3}\pi r^3$. Which average pressure does the object exert on the table?

  1. $\dfrac{1}{3}\rho r^2$
  2. $\dfrac{1}{3}\rho r^2g$
  3. $\dfrac{2}{3}\rho r$
  4. $\dfrac{2}{3} \rho rg$
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D Correct answer
Explanation

Pressure = Force / Area. Force = Weight = mass * g = (density * volume) * g. Volume of hemisphere = (2/3)*pi*r^3. Area of base = pi*r^2. Pressure = (rho * (2/3)*pi*r^3 * g) / (pi*r^2) = (2/3)*rho*r*g.

AI explanation

Pressure is defined as the object's weight divided by its contact area with the table. The weight of the hemisphere is its volume multiplied by density and gravity, calculated as W = (2/3) * pi * r^3 * rho * g, and the flat circular contact area is A = pi * r^2. Dividing the weight by this area gives the average pressure P = [ (2/3) * pi * r^3 * rho * g ] / pi * r^2, which simplifies to P = (2/3) * rho * r * g.

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