Question

The densities of spirit is X g$c{m}^{-3}$. Find [10 X].{where ,[] is a step function}

• A. $0$
• B. $7$
• C. $8$
• D. $9$

Answer 1

Answer: (C)

$8$

Let the densities of water, wood and spirit are $\rho ,{\rho }_w,{\rho }_s$
Let $A$ be the area of the wooden block
Total volume of the wooden block $=15A$
Mass of wood = mass of water displaced by wood
$V\times {\rho }_w\times g=A\times 10\times \rho \times g$
$\Rightarrow {\rho }_w=\frac{A\times 10\times \rho \times g}{V\times g}$ $=0.667g/c{m}^3$

Mass of wood = mass of then spirit displaced.
$V\times {\rho }_w\times g=A\times 12\times {\rho }_s\times g$
$\Rightarrow {\rho }_s=0.833g/c{m}^3$ (Approximately)