Answer all the questions in the spaces provided. (b) A smooth pebble, made from uniform rock, has the shape of an elongated sphere as shown in [Fig. 1.1]. The length of the pebble is L. The cross-section of the pebble, in the plane perpendicular to L, is circular with a maximum radius r. A student investigating the density of the rock makes measurements to determine the values of L, r and the mass M of the pebble as follows: L = (0.1242 ± 0.0001)m r = (0.0420 ± 0.0004) m M = (1.072 ± 0.001)kg.

1. (a)Define density.[1]
2. (b)(i)State the name of a measuring instrument suitable for making this measurement of L.[1]
3. (b)(ii)Determine the percentage uncertainty in the measurement of r.[1]
4. (c)(i)The density ρ of the rock from which the pebble in (b) is composed is given by ρ = Mrⁿ / kL where n is an integer and k is a constant, with no units, that is equal to 2.094. Use SI base units to show that n is equal to –2.[2]
5. (c)(ii)Calculate the percentage uncertainty in ρ.[3]
6. (c)(iii)Determine ρ with its absolute uncertainty. Give your values to the appropriate number of significant figures.[3]

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