Question

In: Physics

A block of wood of uniform density floats so that exactly three-quarters if it’s volume is...

A block of wood of uniform density floats so that exactly three-quarters if it’s volume is underwater. The density of water is 1000 kg/m^3. What is the density of the block?

Expert Solution

_b = density of the block

_w = density of the water = 1000 kg/m³

V = Volume of the block

mass of the block is given as

m = mass of block = Volume x density

m = _b V eq-1

V' = Volume of the block inside the water = 3V/4 = 0.75 V

force of buoyancy on the block is given as

F_b = _w V' g

F_b = (0.75)_w V g eq-2

since the block is floating , the force of buoyancy in upward direction balances the weight in down direction

F_b = F_g

using eq-2 and eq-1

(0.75)_w V g = mg

(0.75)_w V g = _b Vg

_b = (0.75) _w

_b = (0.75) (1000)

_b = 750 kg/m³

genius_generous answered 1 year ago

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