Question

Objects submerged in a liquid appear to have a smaller weight. One way to explain this is that there is a difference in pressure on the top and bottom surfaces. Knowing the relationship between pressure and force. Calculate the difference in the weight of the block in water compared to its weight in the air.

The block is a cuboid, with horizontal faces of area $= 2 m^{2}$ .

The depth of the block is $= 1 m$ .

It is submerged in water, of density $= 1000 kg m^{- 3}$ .

The bottom of the block is at a depth of $6 m$ .

Accepted Answer

Given:

The block is a cuboid, with horizontal faces of area, $A = 2 m^{2}$ .

The depth of the block is, $h_{1} = 1 m$ .

It is submerged in water of density, $ρ = 1000 kg m^{- 3}$ .

The bottom of the block is at a depth, $h_{2} = 6 m$ .

By calculating the Buoyant force at the top and the bottom, we can find the difference in weight of block when compared to that in air.

Weight of the block in water, $W_{1} = h_{1} ρ g A = 1 \times 1000 \times 9.8 \times 2 = 19600 N$ .

Weight of the block in air, $W_{2} = h_{2} ρ g A = 6 \times 1000 \times 9.8 \times 2 = 117600 N$ .

The difference in weight of block when compared to that in air is $W_{2} - W_{1} = 117600 - 19600 = 98000 N$ .

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