A vessel in the shape of a truncated cone, which is narrower at the top and wider at the base, has a base area A . It is filled with a liquid of density up to a height h . If the total mass of the liquid in the vessel is M , how does the force F exerted by the liquid on the base of the vessel compare to the true weight of the liquid Mg ?

Step-by-step solution

The pressure P exerted by the liquid on the base of the vessel is given by P = g h . The force F exerted by the liquid on the base is F = P A = g h A . Because the vessel is narrower at the top and wider at the base, its actual volume V is less than the volume of a cylinder with the same base area A and height h (i.e., V The total mass of the liquid is M = V . Since V Therefore, the force exerted on the base is greater than the true weight of the liquid ( F > Mg ). This is a classic example of the hydrostatic parad