Archimedes’ principle with worked examples

This article reviews Archimedes’ principle and elaborates on the idea with three fully solved examples. The reader is encouraged to attempt the problems on their own before checking the solution.

Consider a container A of fluid at rest, as shown in the figure below. Since the fluid is at rest the net force on any part of the fluid is zero. Let us draw an imaginary boundary around some region of the fluid, as shown in the figure. This parcel of fluid has a weight \rho_{\rm fl} V g, where \rho_{\rm fl} is the density of the fluid and V is the volume of the parcel. …

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Buoyancy of connected objects

JEE Advanced 2013 Paper 1, Question 12

A solid sphere of radius R and density \rho is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3 \rho. The complete arrangement is placed in a liquid of density 2 \rho and is allowed to reach equilibrium. The correct statement(s) is (are)

  1. the net elongation of the spring is \frac{4 \pi R^{3} \rho g}{3 k}.
  2. the net elongation of the spring is \frac{8 \pi R^{3} \rho g}{3 k}
  3. the light sphere is partially submerged.
  4. the light sphere is completely submerged.


Recall that the buoyant force experienced by …

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An adiabatic bubble

IIT-JEE 2008 Paper 1, Question 38,39,40

A small spherical monoatomic ideal gas bubble \left(\gamma=\frac{5}{3}\right) is trapped inside a liquid of density \rho_{\ell} (see figure below). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_{0}, the height of the liquid is H and the atmospheric pressure is P_{0} (Neglect surface tension).

Rendered by

1. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

  1. Only the force of gravity
  2. The force due to gravity and the force due
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