A cubical block of wood of edge 3 cm floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. Find the maximum weight that can be put on the block without wetting it. Density of wood =`800 kgm^-3` and spring constant of the spring `=50Nm^-1 Take g=10ms^-2`.
,

Explanation

The specific gravity of the block =0.8. Hence the height inside water `=3cmxx0.8=2.4cm`. The height outside water `=3cm-2.4=0.6cm`. Suppose the maximum weight that can be put without wetting it is W. The block in this case is completely immersed i the water. The volume of the displaced water
`=volume of the block `=27xx10^-6m^3`
Hence the force of buoyacy.
`=(27xx10^-6m^I3)xx(1000kgm^-3)(10ms^-2)`
`=0.27N`
The spring is compressed by 0.6 cm and hence the upward foce exerted by the spring.
`=50 Nm^-1xx0.6cm=0.3N`
the forece of buoyancy and the spring force taken together balance the weight of the block plus the weight w put on the block. The weight of the block is
`W'=(27xx10^-6m)xx(800kgm^-3)xx(10ms^-2)`
`=0.22N`
Thus, `W=0.27N+0.3N-0.22N`
`=0.35N`