A wooden block of cross-sectional area 10cm^(2) is floating vertically on water. The volume of the immersed portion of the block is 200cm^(3). The block is depressed slightly inside water and then released. Calculate the time period of vibration of the block.

A wooden block of cross-sectional area 10cm^(2) is floating vertically

1.	A wooden block of cross-sectional area 10cm^(2) is floating vertically on water. The volume of the immersed portion of the block is 200cm^(3). The block is depressed slightly inside water and then released. Calculate the time period of vibration of the block.
Answer» SOLUTION :Volume of displaced water = `200CM^(3)` `therefore" "` Mass of displaced water = 200 g, and mass of the wooden BLOCK = 200 g Let the block be depressed inside water through x cm and then RELEASED. `therefore` Upward restoring force on the block, `F=10x xx1xxg=10xg` `therefore` Acceleration of the block, `a=F/m=(10xg)/200=(xg)/20` `therefore` Time period of vibration of the block, `T=2pisqrt(x/a)=2pisqrt(20/g)=2pisqrt(20/980)=0.897s`.