a block of wood floats in a liquid of density of 0.8 g cm cube with one fourth of its volume submerged. find the density of wood.
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A block of wood floats in liquid of density 0.8 g/cm³ with one Fourth of its volume submerged.
Let the volume of wood is V cm³
and density of wood is d g/cm³
Then, weight of block of wood = Vdg = V × d × 980 Dyne [ g is Acceleration due to gravity it is 980 cm/s²]
The block floats in a liquid of density 0.8g/cm³ with 1/4th of its volume submerged. Hence, upward buoyancy force acting on the block is the weight displaced of liquid = 1/4 ( V × density of liquid × g)
= 1/4( V × 0.8 × 980)
Now, by condition of floatation ,
weight of block = buoyancy force acting on the block
V × d × 980 = 1/4 × ( V × 0.8 × 980)
d = 0.8/4 = 0.2g/cm³
Hence, the density of wood is 0.2g/cm³
Let the volume of wood is V cm³
and density of wood is d g/cm³
Then, weight of block of wood = Vdg = V × d × 980 Dyne [ g is Acceleration due to gravity it is 980 cm/s²]
The block floats in a liquid of density 0.8g/cm³ with 1/4th of its volume submerged. Hence, upward buoyancy force acting on the block is the weight displaced of liquid = 1/4 ( V × density of liquid × g)
= 1/4( V × 0.8 × 980)
Now, by condition of floatation ,
weight of block = buoyancy force acting on the block
V × d × 980 = 1/4 × ( V × 0.8 × 980)
d = 0.8/4 = 0.2g/cm³
Hence, the density of wood is 0.2g/cm³
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