Question

A block of wood weighs 60g in air.a lead sinker weighs 70g in water.The sinker is attached to the wood and both together weigh 65g in water. Find the relative density of the wood

Answer 1

Question #77654, Physics / Other

A block of wood weighs 60g in air. A lead sinker weighs 70g in water. The sinker is attached to the wood and both together weigh 65g in water. Find the relative density of the wood

Solution

$$(\rho_{lead} - \rho_{water})V_{lead} = 70\,g$$ $$V_{lead} = \frac{70}{(\rho_{lead} - \rho_{water})}$$ $$(\rho_{wood})V_{wood} = 60\,g$$ $$V_{wood} = \frac{60}{(\rho_{wood})}$$ $$(\rho_{lead})V_{lead} + (\rho_{wood})V_{wood} - \rho_{water}(V_{lead} + V_{wood}) = 65\,g$$

Thus,

$$(\rho_{lead}) \frac{70}{(\rho_{lead} - \rho_{water})} + (\rho_{wood}) \frac{60}{(\rho_{wood})} - \rho_{water} \left( \frac{70}{(\rho_{lead} - \rho_{water})} + \frac{60}{(\rho_{wood})} \right) = 65\,g$$ $$(\rho_{lead}) \frac{70}{(\rho_{lead} - \rho_{water})} + (\rho_{wood}) \frac{60}{(\rho_{wood})} - \rho_{water} \left( \frac{70}{(\rho_{lead} - \rho_{water})} + \frac{60}{(\rho_{wood})} \right) = 65\,g$$ $$70 - 60 \left( \frac{\rho_{water}}{\rho_{wood}} - 1 \right) = 65$$ $$60 \left( \frac{\rho_{water}}{\rho_{wood}} - 1 \right) = 5$$ $$\frac{\rho_{water}}{\rho_{wood}} - 1 = \frac{5}{60} = \frac{1}{12}$$ $$\frac{\rho_{water}}{\rho_{wood}} = 1 + \frac{1}{12} = \frac{13}{12}$$

The relative density of the wood is

$$\frac{\rho_{wood}}{\rho_{water}} = \frac{12}{13} \approx 0.923$$

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