Solution:

Given,

Length of the block = 2 m
Width of the block = 1 m
Depth of the block = 1 m
Depth of immersion = 0.5 m
Density of water = 10 kN/m³

Weight of the block = ?

Formula used:

Buoyancy force = Weight of fluid displaced by the object

Let's first find out the volume of the block submerged in water.

Volume submerged = Length x Breadth x Depth of immersion
= 2 x 1 x 0.5
= 1 m³

Volume of the entire block = Length x Breadth x Depth
= 2 x 1 x 1
= 2 m³

Volume of the block above water = Volume of the entire block - Volume submerged
= 2 - 1
= 1 m³

The weight of the water displaced by the block is given by:

Weight of water displaced = Volume of displaced water x Density of water
= 1 x 10
= 10 kN

Now, let's find out the weight of the block.

Buoyancy force = Weight of fluid displaced by the object
Weight of fluid displaced by the object = Buoyancy force

The weight of the block = Buoyancy force + Weight of block

As the block is floating in water, the buoyancy force acting on the block is equal to the weight of the water displaced by the block.

Therefore, Buoyancy force = Weight of water displaced = 10 kN

Weight of the block = Buoyancy force + Weight of block
Weight of the block = 10 kN + Weight of block

Weight of the block = Density of block x Volume of the block x g

As the block is homogeneous, its density is constant throughout.

Density of the block = Weight of the block / Volume of the block
Weight of the block = Density of the block x Volume of the block

Weight of the block = (Weight of the block / Volume of the block) x Volume of the block x g

Weight of the block = Weight of the block x g

g = Acceleration due to gravity = 9.81 m/s²

Therefore, Weight of the block = (10 / 1) x 9.81 = 98.1 kN

Hence, the weight of the block is 98.1 kN.

1*2*.5*10 =10kn