Question

yBLEMS FOR TOPIC 3 ASSIGNMENT QUESTIONS AND PROBLEMS FOR TOPIC 3.1 A student was supplied with a stop watch, two metre rules and a simole pendulum suspended from a ceiling and was asked to measure the heihple the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different lengths of the Since he was unable to measure the length of the pendulum direer measured the height of the centre of the pendulum bob above the floor. He ight of obtained the results tabulated below Height of bob above floor Time for 50 oscillations 155.3 400 148.8 600 42.2 800 134.0 1000 127.4 1200 119.2 1400 110.5 1600 The period T of the pendulum of length ? is given by T = 2π where g is the acceleration due to gravity. But e= h-h where H is the height of the ceiling and h is the height of the centre of the pendulum above the floor. Therefore Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that g 9.8 ms-2 (g could be obtained from the slope of the graph). Having obtained your values for H, answer the following (a) Which value of H do you consider to be the least accurate? Give reasons for your choice and explain how the accuracy could have been improved (b) Why was the bob set swinging through a small angle? 208

Answer 1

Page No. 2 2. 2- 2. 2 2. 412 = 0106 9 2.

This is the data that we have put in: (1).164,9.6472 (2).246,8.856 (3).328,8.088 (4).41,7.1824 (5).492,6.492 (6).574,5.683 (7).656,4.88 Note: x values multiplied by .41, y values divided by 50 and then squared Obtained graph: ample size: Mean x (Xx): 0.41 Mean y (y): 7.2612285714286 Intercept (a): 11.2333 Slope (b): -9.6879790940767 Regression line equation: y 11.2333-9.6879790940767x 9 7 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

(a)Data point three gives the least accurate value of H as it lies most away(visibly) from the line of best fit. Accuracy can be improved by using recently and accurately calibrated instruments. (b) The bob was set swinging through a small angle because, at small angles, the sin of the angle is the angle itself Moreover, taking large angles would increase T which would mean even more inaccuracies