(a)With divisions every 0.1 cm, the uncertainty is half the smallest division.

(b)Period = total time ÷ number of oscillations.

(c)Timing one oscillation makes any reaction-time error (~0.2–0.3 s) a large fraction of the measurement. Spreading the same error over 20 oscillations, then dividing, makes the error per oscillation much smaller.

(a)Volume = length × width × height.

(b)Density = mass ÷ volume.

(c)2.8 g/cm³ is closest to the density of aluminium (≈2.7 g/cm³).

(a)Period = time ÷ number of oscillations.

(b)Rearranging T = 2π√(L/g) gives g = 4π²L / T².

(a)A micrometer screw gauge (or digital calipers) reads to 0.01 mm, far more precise than a ruler's 1 mm divisions, which matters for a thin wire.

(b)Partly fill a measuring cylinder with water and record the volume (V1). Lower the stone in on a thread so it is fully submerged, and record the new volume (V2). The volume of the stone is V2 − V1.

(a)1 km = 1000 m, so multiply by 1000.

(a)1 s = 1000 ms, so divide by 1000.

(a)Add the thimble reading (divisions × 0.01 mm) to the main scale reading.

(a)Percentage uncertainty = (uncertainty ÷ measurement) × 100.

(a)Read the meniscus at eye level, and view it directly from the front to avoid parallax error.

(a)Placing the ruler vertically next to the object without support makes it easy for the ruler to lean or tilt, causing an inaccurate reading. A set-square held against a flat surface keeps the ruler perfectly vertical.