Question

A 500g circular pan 20cm in diameter has straight sides 6cm high and is made from metal of negligible thickness. To what maximum depth can the pan be filled with water and still float on water? the density of water is 1g/cm^3

Answer 1

According to Archimidies, any object, wholly or partially immersed in a fluid, buoyed up by a force equal to the weight of the fluid displaced by the object.

weight of the liquid dispaced = weight of the pan with water upto height h;

volume(displaced)*density*g = (500*g) + (pi*(10)² *h)*density*g;

as total volume of the pan is equal to volume of water displaced, therefore;

(pi*(10)² * 6* 1)*g = 500*g +  (pi*(10)² *h)* 1* g;

h = 4.408 cm (max depth can be filled)

weight of the pan = V*density;

= pi*(.10)² *h