Expt : 5                                              Simple pendulum

 

Aim :

          To determine the acceleration due to gravity using a simple pendulum and to determine the length of seconds pendulum

 

Apparatus :

           Retort stand, metallic bob, string, stop watch and a meter scale

 

Formula:

             (a) Time period of oscillation of a simple pendulum

                                 T = 2p √(L / g)

                   therefore acceleration is given by

                                g = 4p2  ( L / T2 )

             (b) Seconds pendulum has a time period of 2 seconds

Diameter of the sphere

S.No. MSR VC VC x LC Actual reading (cm)
1 1.9 4 0.04 1.94
2 1.9 3 0.03 1.93
3 1.9 5 0.05 1.95
4 1.9 4 0.04 1.94
5 1.9 3 0.03 1.93

                                                                                                                                                      Average : 1.94 cm

radius of the sphere = D/2

                              = 1.94 / 2

                              = 0.97 cm

 

 L/T2 for simple pendulum

S.No. length (L) Time for 20 oscillations T =  t / 20 T2 L / T2
trial 1 trial2 mean ( t )
1 50 28 29 28.5 1.41 2.01 24.8
2 60 30 31 30.5 1.54 2.40 24.9
3 70 33 33 33.0 1.66 2.77 25.2
4 80 35 36 35.5 1.78 3.20 25.0
5 90 38 38 38.0 1.90 3.62 24.8
6 110 41 42 41.5 2.08 4.36 25.1

                                                                                                                                                                          Average :   25.05 cm s-2

Acceleration due to gravity is given by

                                g = 4 p2 ( L / T2 )

                                   =  4 x 3.14 x 3.14 x 25.05

                                   = 988.0 cm s-2

 

[Click here for the sample L - T2 graph]

[Click here for the sample L - T graph]

Acceleration due to gravity from graph

                            g =  4 x p2 x cot (q)

                              =  4 x 3.14 x 3.14 x 25

                              =  986.9 cm s-2

Result

        (a)  Acceleration due to gravity from table is  : 988.0 cm s-2

          (b)  Length of seconds pendulum is               : 100 cm

          (c)  Acceleration due to gravity from graph is : 986.9 cm s-2

          (d)  Percentage of error in measurement is     : 0.816  %