Question

Question #93122

Answer 1

I am not sure I got the question right but....it depends upon the materials your blocks are made of.

Explanation:

We can refer to Archimedes’ Principle and the fact that an object immersed in a fluid receives am upward force equal to the weight of the displaced fluid.

Consider a block of lead and a block of wood of the same volume. They will displace the same amount of water so they will receive the same upward force as Archimedes confirms...BUT this upward force will perfectly balance the WEIGHT of the wooden block while it will not balance the WEIGHT of the one made of lead!
The block of lead will sink because the buoyant force will not be able to sustain it.
Basically, DENSITY will be a critical parameter to decide whether your block floats or not.

If you want your block of lead to float you need to increase the upward force but to do that you need to displace more water and to do that you need to shape your block into, say, a kind of very thin and very large foil with borders (basically....a big empty ball or buoy!)

Answer 2

Let V represents the volume of any of the sevaral blocks of same volume ,`d_"block"` represents the density of the material of a particular block and `g` represents the accelertion due to gravity.

Then weight or downward gravitational pull on the block will be

`Wdarr=Vxxd_"block"xxg`

If `d_"water"` represents the density of water, then the maximum buoyant force (upward) that can be produced is obtained by the commplete immersion of the block in water as buoyant force is proportional to the immersed volume of the body in the fluid.

So the maximum buoyant force on the block will be equal to the weight of displaced water when the block is completely immersed in it and this will be

`B_"max"uarr=Vxxd_"water"xxg`

If `" " Wdarr > Buarr`

#=> Vxxd_"block"xxg > Vxxd_"water"xxg#

#=> d_"block" > d_"water" color(red)(->"the block will sink"#

Again if `" " Wdarr <= Buarr`

#=> Vxxd_"block"xxg <= Vxxd_"water"xxg#

#=> d_"block" <= d_"water" color(green)(->"the block will float"#

Conclusion

So density of the block under consideration is the determining factor. Those blocks having higher o density than density of water will sink in water and those having equal or less density than water will float. Here volume of the block does not matter.