Irodov Problem 4.19

There are three forces acting on the pendulum bob, i) the gravitational force mg, acting vertically downwards ii) the buoyant force acting on the bob vertically upwards and iii) the tension in the string T. Since the density of the fluid is times less denser, the buoyant force acting on the bob is .

The net force acting on the bob in the direction perpendicular to the thread is and hence the torque acting on the bob about the point of suspension is given by . Assuming that the pendulum bob is so small that it can be considered to be a point mass, its moment of inertia about the point of suspension is given by . Hence we have,







For small values of we have,





From two it is clear that the oscillations are simple harmonic with a period of