Question

A block of wood has a mass of $25g$. When a $5g$ metal piece with a volume of $2c{m}^3$ is attached to the bottom of the block, the wood barely floats in water. What is the volume $\left(\text{in}c{m}^3\right)$ of the wood?

Answer 1

Draw a diagram of given problem.
calculate volume of wood.
Given,
Mass of wooden block, $M=25g$
Mass of metal piece, $m=5g$
Volume of metal piece, $V=2c{m}^3$
Weight = upthrust
$(m+M)g={\rho }_w[V+(2\times {10}^{-6}]g$
$V=\frac{m+M}{{\rho }_w}-2\times {10}^{-6}$
$V=\frac{0.025kg+0.005kg}{1000}-2times{10}^{-6}$
$V=(25+5){10}^{-6}-2\times {10}^{-6}$
$V=28\times {10}^{-6}{m}^3=28c{m}^3$
Final answer: $\left(28\right)$