Physics A Level Sciences Worksheets, Questions and Revision

A student measures the diameter of a small ball bearing with a micrometer of resolution 0.01 mm, obtaining a mean diameter of 6.20 mm from several readings. Calculate the volume of the ball bearing, using V = (4/3) x pi x r^3, and express the answer with its absolute uncertainty.

1. Find the absolute uncertainty in the diameter: half the micrometer's resolution = 0.01 / 2 = 0.005 mm.
2. Convert to a percentage uncertainty: (0.005 / 6.20) x 100 = 0.081%. This is also the percentage uncertainty in the radius, since dividing by the constant 2 does not change a percentage.
3. Since V depends on r^3, multiply the percentage uncertainty by 3: percentage uncertainty in V = 3 x 0.081% = 0.24%.
4. Calculate the radius and volume: r = 3.10 mm, so V = (4/3) x pi x (3.10)^3 = 124.8 mm^3.
5. Convert the percentage uncertainty in V to an absolute uncertainty: 124.8 x 0.0024 = 0.3 mm^3.
6. Final answer: V = (124.8 plus or minus 0.3) mm^3.