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Home » A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute SHM with a time period where m is mass of the body and ρ is the density of the liquid.
A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute SHM with a time period where m is mass of the body and ρ is the density of the liquid.
CBSE | Class 11 | NCERT Exemplar | Oscillations | Physics
A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute SHM with a time period where m is mass of the body and ρ is the density of the liquid.

Answer:

Let us consider that the verticle displacement at the equilibrium position is   {{x}_{0}}

At equilibrium

A{{x}_{0}}\rho g
When it is displaced further by a displacement x, the buoyant force is A({{x}_{0}}+x)\rho g
The net restoring force then becomes,

F=A({{x}_{0}}+x)\rho g-mg=A\rho gx

  [We have taken mod value]
So, we get

T=2\pi \sqrt{\frac{m}{A\rho g}}

i

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