**Question:**

A wooden block of mass $0.5 \mathrm{~kg}$ and density $800 \mathrm{~kg} / \mathrm{m}^{3}$ is fastened to the free end of a vertical spring of spring constant 50 $\mathrm{N} / \mathrm{m}$ fixed at the bottom. If the entire system is completely immersed in water, find

(a) the elongation (or compression) of the spring in equilibrium and

(b) the time-period of vertical oscillations of the block when it is slightly depressed and released.

**Solution:**