Sand has a density of $\rho = 2600 \frac{kg}{m^3}$. A typical grain of sand is spherical with a radius $R = 50 \mu m$.
Question 1. The mass of a single grain of sand is closest to
A 1 nanogram
B 1 picogram
C 1 microgram
D 1 milligram
E 1 gram
Question 2. You have a bucket with one kilogram of sand. Imagine that you could take all the sand from the bucket and separate the grains into a single straight line so that they were just barely touching (like a pearl necklace). About how long would your sand necklace be?
A 73,000 m
B 7,300 m
C 7,300,000 m
D 73 m
E 730 m
F 7.3 m
G 730,000 m
Question 3. Convert the density of sand to the units of $\frac{\mu g}{(\mu m)^3}$. In these units, $\rho$ has a numerical value of $2.6 \times 10^{\alpha}$. What is $\alpha$?
Question 4. If each individual sand grain has a radius $R$ that was 10 times larger than the information given above, how would the length of the sand necklace in Question 2 change? The length of the sand necklace would
A increase by a factor of 10
B increase by a factor of 100
C decrease by a factor of 10
D decrease by a factor of 100
E stay the same
Hint: Be careful. The size of a sand grain may have changed, but you still only have 1 kg of sand.
