Question

A sample of sand has a volume of 1000 ml in its natural state. Its minimum volume when compacted is 750 ml. When gently poured into a measuring cylinder, its possible maximum volume is 1320 ml. What is the relative density?

• A. 56
• B. 52
• C. 58
• D. 60

Answer 1

The correct option is A 56

$V=10ml,$

$V_{min}=750ml,$

$V_{max}=1320ml$

$e=Voidratio=\frac{V_V}{V_S}$

$Hence,V_s=constantforallconditiononly{V}_{v}changes$.
$Let,V_s=x$

$e=\frac{V_v}{V_s}=\frac{V-V_s}{V_s}=\frac{V}{V_s}-1$

$Fornaturalstate,e=\frac{100}{x}-1$

For maximum compacted state,
$e_{max}=\frac{1320}{x}-1$
For minimum compacted,

$e_{min}=\frac{750}{x}-1$

$\Rightarrow \mathrm{Re}lativedensity=\frac{e_{max}-e}{e_{max}-e_{min}}\times 100$

$=\frac{(\frac{1320}{x}-1)-(\frac{1000}{x}-1)}{(\frac{1320}{x}-1)-(\frac{750}{x}-1)}\times 100$

$=\frac{\frac{320}{x}}{\frac{570}{x}}\times 100=\frac{320}{570}\times 100=56.14\%$