Question

A block of wood of length 40 cm and an area of cross section 15 cm² floats in water with 3/8 of its length above its water. What is the density of wood ? (density of water = 1 g/cm³)
(A) 0.256 g/cm³
(B) 0.526 g/cm³
(C) 0.625 g/cm³
(D) 0.650 g/cm³
​Kindly do not give any link or hint for the above question.

Answer 1

Dear Student ,
Here in this case ,
$$\begin{gathered} Densityowater=1g/c{m}^3 \\ Volumeofthebodyinsidethewater=\left(1-\frac{3}{8}\right)\times 40\times 15c{m}^3=\frac{5}{8}\times 40\times 15c{m}^3 \\ Therefore,massofthefluiddisplaced, \\ {m}_f=1g/c{m}^3\times \frac{5}{8}\times 40\times 15c{m}^3 \\ =\frac{5}{8}\times 40\times 15gm \\ Thereforethedensityofthebody=\rho =\frac{m}{V}=\frac{\frac{5}{8}\times 40\times 15c{m}^3}{40\times 15c{m}^3}=\frac{5}{8}g/c{m}^3=0·625g/c{m}^3 \end{gathered}$$
Regards