Question

A solid cylinder of mass M=10 kg and cross-sectional area A=20 cm${}^2$ is suspended by a spring of force constant k=100 N/m and hangs partially immersed in water. Calculate the period of small oscillations of the cylinder.

Answer 1

In such situation upthmst also behaves like a spring force of force constant$=\rho Ag$
$k_{net}$ in the given situation is $(k+\rho Ag)$
$\therefore$ $T=2\pi \sqrt{\frac{m}{k+\rho Ag}}$
$=2\pi \sqrt{\frac{10}{100+1000\times 20\times {10}^{-4}\times 10}}$
$=1.8$ s