What does density mean?
State the name of a measuring instrument that would be suitable for this measurement of $L$.
Find the percentage uncertainty for the measurement of $r$.\n\npercentage uncertainty $=$ ........................................ $\%$
A pebble with a smooth surface, made of uniform rock, has the form of an elongated sphere as shown in Fig. 1.1. Its length is $L$. The pebble’s cross-section, in the plane at right angles to $L$, is circular with a largest radius $r$. A student studying the density of the rock measures $L$, $r$ and the mass $M$ of the pebble as follows: $L = (0.1242 \pm 0.0001)\,\text{m}$, $r = (0.0420 \pm 0.0004)\,\text{m}$, $M = (1.072 \pm 0.001)\,\text{kg}$.
The density $\rho$ of the rock forming the pebble in (b) is given by $\rho = \dfrac{M r^{n}}{k L}$, where $n$ is an integer and $k$ is a constant with no units equal to $2.094$.
Use SI base units to demonstrate that $n$ is $-2$.
Calculate the percentage uncertainty in $\rho$.
Determine $\rho$ together with its absolute uncertainty. Present your values to the correct number of significant figures.