When a cylindrical wooden piece weighing 75 gwt is made to float in water, `25%` of the total volume of the water.
Find the extra force in gwt required to be applied on the piece downwards so that the piece gets immersed in water completely

Explanation

According to the law of floatation,
weight of the floating body = weight of the liquid displaced
`rArr("density of the body")/("density of the liquid")`
`=("volume of the body inside liquid")/("total volume of the body")`
Given `25%` of the body is above the water surface
`rArr` fraction of the body inside water = `75%`
`:.("Pwooden piece")/("Pwater")=75%`
`rArr" Pwooden piece"=0.75" g cm"^(-3)`
Given weight of the wooden piece = 75 gwt
`:.` volume of the wooden piece
`("75 gwt")/("0.75 g cm"^(-3))=100cm^(3)`
volume of water displaced by the body
= fraction of the body inside water x volume of the woodent piece
`=0.75xx100=75cm^(3)`
`:." remaining volume"=25cm^(3)`
If the body has to be completely immersed in water, the extra force required
= weight of `25cm^(3)` of water = 25 gwt