Answers · Measuring and the pendulum
Measuring and the pendulum — final check key
Check meaning, not exact wording. These are teaching points, not official Cambridge marks.
1. SK1 · Final check
Model answer. (a) Count 50 drops into the cylinder standing on a flat bench. With your eye level with the water surface, read the bottom of the meniscus. (b) Volume of one drop = 2.4 cm³ ÷ 50 = 0.048 cm³. (c) One drop is about 0.05 cm³, a quarter of the smallest division (0.2 cm³), so it cannot be read directly. Fifty drops make a volume that can be read, and the reading error is shared out over 50 drops.
A full answer includes
- (a) I said to stand the cylinder on a flat surface, put my eye level with the water and read the bottom of the meniscus.
- (b) I calculated 2.4 cm³ ÷ 50 = 0.048 cm³.
- (c) I explained that one drop (about 0.05 cm³) is smaller than one division (0.2 cm³), so it cannot be read; 50 drops give a readable volume and the reading error is shared over 50 drops.
Also accept
- (a) flat bench, eye level, bottom of meniscus; (b) 0.048 cm³; (c) one drop is smaller than a division; the error is shared over 50 drops.
Watch for
- “Read the level where the water touches the glass.” — Read the bottom of the meniscus for water.
- “Measuring 50 drops removes the reading error.” — It reduces the error per drop by sharing it over 50 drops; it does not remove it.
2. SK2 · Final check
Model answer. (a) Use a metre rule to measure from the pivot to the centre of the bob, with your eye level with the mark. (b) Release the bob from a small angle; start the stop-clock as the bob passes a marker at its lowest point and count that as zero; stop at the 20th pass in the same direction; repeat and take the mean; divide by 20. (c) Period = 35.9 s ÷ 20 = 1.80 s. (d) The period increases with length, but not in proportion: four times the length gives only twice the period, so the graph is a curve, not a straight line through the origin.
A full answer includes
- (a) I measured from the pivot to the centre of the bob with a metre rule, eye level with the mark.
- (b) I timed 20 oscillations, starting and stopping as the bob passes a marker at its lowest point, counting from zero, and repeated and averaged.
- (c) I calculated 35.9 s ÷ 20 = 1.80 s (1.795 s).
- (d) I stated that a longer pendulum has a longer period, but the period is not proportional to the length (four times the length only doubles the period).
Also accept
- (a) pivot to centre of bob; (b) many oscillations, marker at the lowest point, count from zero, repeat; (c) 1.80 s (1.8 s); (d) increases, not proportional.
Watch for
- “Measure the length of the string only.” — The length of a pendulum runs from the pivot to the centre of the bob, so include half the bob.
- “Double the length, double the period.” — The period grows more slowly than the length: four times the length doubles the period.