The diameter of a solid metal sphere is measured using a micrometer screw gauge.

Question 26

The diameter of a solid metal sphere is measured using a micrometer screw gauge. The diagram shows an enlargement of the shaft of the micrometer screw gauge when taking the measurement.

The mass of the sphere is 0.450 g.

What is the density of the metal used to make the sphere?

A 965 kg m^-3                    B 1340 kg m^-3                 C 7720 kg m^-3                                 D 10 700 kg m^-3

Reference: Past Exam Paper – June 2016 Paper 11 Q15

Solution:

Answer: C.

From the micrometer reading,

Diameter of sphere = 4.50 + 0.31 = 4.81 mm

Volume of sphere = 4/3 πr³ = 4/3 π(d/2)³ = 4πd³ / 24

Volume of sphere = πd³ / 6 

Density = mass / volume

The quantities need to be in SI units.

Density of metal used = (0.450×10^-3) / [π × (4.81×10^-3)³ / 6]

Density = 7723 ≈ 7720 kg m^-3