A wooden cylinder of mass 20 g and area of cross-section `1 cm^(2)` , having a piece of lead of mass 60g attached to its bottom, floats in water. The cylinder is depressed and then released. The frequency of oscillation is `( N )/(pi ) S^(-1)`. Find the value of N. [Neglect the volume of water displaced by the lead piece, take `g =9.8m//s^(2) `,density of water `rho_(w ) = 1 g cm^(-3) ` ]

Answer

`1.75`

Explanation

Suppose that the loaded wooden block sinks upto a height h. Then,
weight of water displaced by the block
= weight of the block with lead
If a is area of cross-section of the block and o, the density of water, then
`a h sigma a=(M+m)g`
or `h=(M+m)/(a sigma)`
`=(20+60)/(1xx1)=80m`
( `:.` density of water `=1 gcm^(-3))`
Now for small displacement .z. from equilibrium