Question

A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. A simple pendulum can be approximated by a small metal sphere which has a small radius and a large mass when compared relatively to the length and mass of the light string from which it is suspended. If a pendulum is set in motion so that is swings back and forth, its motion will be periodic. The time that it takes to make one complete oscillation is defined as the period T.

T=2πlg

(1)

T2=4π2g l

(2)

Where l is the length of the pendulum and ? is the acceleration due to gravity.

In an experiment to study the dependence of the periodic time T on the length of the pendulum sting, a student has collected the data listed in the following table.

Length , l (cm)	T (sec.)
10	0.6
15	0.75
20	1
25	1.2
30	1.4
35	1.3
40	1.5
45	1.55
50	1.6
55	1.65
60	1.68
65	1.7
70	1.75
75	1.8
80	1.9
85	1.95
90	2
100	2.2

Using the data in the above table, graph the relation between the square of periodic time ?² vs the length l. Using Equation 2, find the gravity constant (?) from the best fit line.

Attach the graph paper and show all your works on the below space

Answer 1

Length l           ( cm)	Length      (m)	T ( S)	T2
10	0.10	0.60	0.36
15	0.15	0.75	0.56
20	0.20	1.00	1.00
25	0.25	1.20	1.44
30	0.30	1.40	1.96
35	0.35	1.30	1.69
40	0.40	1.50	2.25
45	0.45	1.55	2.40
50	0.50	1.60	2.56
55	0.55	1.65	2.72
60	0.60	1.68	2.82
65	0.65	1.70	2.89
70	0.70	1.75	3.06
75	0.75	1.80	3.24
80	0.80	1.90	3.61
85	0.85	1.95	3.80
90	0.90	2.00	4.00
100	1.00	2.20	4.84

Slope of the graph = (0.9- 0.5)/(4-2.56) = 0.4/1.44 = 0.2778

T² = 4π² x L/g

g = 4π² x( L/ T²) = 4π² x slope =4 x( 3.14)² x 0.2778

g = 10.95 m/s²

NB : Actual graph cannot be uploaded due to big Size . ( more than 2 MB ).So only excel sheet is used