A cube of water with side 10.0 cm floats vertically in water with 4.5 cm its length submerged. Calculate the density of the wood.
[Density of water = 1 g/cm\(^3\); D = 0.090 g/cm\(^3\)]
A
0.090 g/cm\(^3\)
B
0.450 g/cm\(^3\)
C
0.230 g/cm\(^3\)
D
0.0450 g/cm\(^3\)
Verified Correct Answer: B.
Physical Principles & Numerical Solution
Volume of cube = s\(^3\) = 10\(^3\) = 1000cm\(^3\)
Volume of cube submerged = 10 cm x 10 cm x 4.5 cm = 450 cm\(^3\)
Volume of water displaced = volume of cube submerged = 450 cm\(^3\)
Mass of water displaced = 1 cm\(^3\) x 450 cm\(^3\) = 450g (density of water is 1 cm\(^3\))
Mass of cube = V\(_{cube}\) x \(\rho_{cube}\)
But, mass of cube = mass of water displaced
1000 cm\(^3\) x \(\rho_{cube}\) = 450g
\(\rho_{cube}\) = \(\frac{450}{1000}\) = 0.45 g/cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #72041)