A block of wood of uniform density floats so that exactly half ofits volume is u

Question

A block of wood of uniform density floats so that exactly half ofits volume is underwater. What is the density of the block?

A)0.5kg/m3
B)500kg/m3
C)1000kg/m3
D)2000kg/m3
Hint: The buoyant force on the block is equal to the weight of thedisplaced water.
B = rho(water)*(V/2)*g, since only half the volume of theblock displaces water. B exactly balances the weight W = rho(block)*V*g of theblock.
Set W = B and solve for rho(block) with rho(water) = 1000kg/m^3.

A)0.5kg/m3
B)500kg/m3
C)1000kg/m3
D)2000kg/m3
Hint: The buoyant force on the block is equal to the weight of thedisplaced water.
B = rho(water)*(V/2)*g, since only half the volume of theblock displaces water. B exactly balances the weight W = rho(block)*V*g of theblock.
Set W = B and solve for rho(block) with rho(water) = 1000kg/m^3.

Explanation / Answer

   According to Archimedes' principle, when abody just floats, its weight is exactly equal to the weight ofliquid it displaces.    weight of woodenblock   =weight of water displaced    Vw * dw *g   =   V * d *g   =>   dw   =   V* d / Vw       Vw   =   volumeof woodenblock,   V   =   volumeof waterdisplaced   =   Vw /2       d   =   densityof water   =   1.0 *103   kg/m3          densityofwood   dw   =   (Vw/ 2) * 1.0 * 103 /Vw        =   5.00*102   kg/m3   =   500 kg/m3          densityofwood   dw   =   (Vw/ 2) * 1.0 * 103 /Vw        =   5.00*102   kg/m3   =   500 kg/m3

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