A cylindrical piece of cork of density of base area A and height h floats in a liquid of density p_(l). The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hp)/(p_(1)g)) where p is the density of cork. (Ignore damping due to viscosity of the liquid).

A cylindrical piece of cork of density of base area A and height h flo

1.	A cylindrical piece of cork of density of base area A and height h floats in a liquid of density p_(l). The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hp)/(p_(1)g)) where p is the density of cork. (Ignore damping due to viscosity of the liquid).
Answer» <html><body><p></p>Solution :In equilibrium, weight of the cork equals the up <a href="https://interviewquestions.tuteehub.com/tag/thrust-709467" style="font-weight:bold;" target="_blank" title="Click to know more about THRUST">THRUST</a>. When the cork is depressed by an amount x, the net upward <a href="https://interviewquestions.tuteehub.com/tag/force-22342" style="font-weight:bold;" target="_blank" title="Click to know more about FORCE">FORCE</a> is `Axp_(1)g`. Thus the force constant `k = Ap_(1)g `. Using m = <a href="https://interviewquestions.tuteehub.com/tag/ahp-362384" style="font-weight:bold;" target="_blank" title="Click to know more about AHP">AHP</a>, and `T=2pisqrt(m/k)` one gets the given expression.</body></html>