NO EXPERIMENT9 )

Using a simple pendulum, plot L-T and L-T2 graphs. Hence find the effective length of
AIM second's pendulum using appropriate graph.

APPARATUS:
A metre rod, A clamp stand, Stop watch, A brass bob, Fine thread, A rubber cork and Vernier
Callipers
DIAGRAM
Split- A
cork

Clamp
Stand s Split
cork

L=l+r -Thread
L I
Table

Hook
IT
5cm 5cm c.G of
the bob
(a) b)
THEORY AND FORMULA USED
A
simple pendulum consist of a metallic bob and an inextensible
connected to rigid support and other end is connected to hook massless string. The one end of string is
of bob. The oscillations of
vertical plane. pendulum must be in
IfLis length of thread or string from
point of suspension and the surface of metallic bob and r is its radius then
the effective lengths of pendulum is given by
L = l+r
The amplitude of oscillations should be small and in vertical plane.
The expression for time period of pendulum is given by
L
T 27t N:
where g is the acceleration due to gravity at the
place of experiment. T
The time period of oscillation of
pendulum is directly proportional to square root of the length of pendulum
i.e.,
Toa L
Thus the graph plotted between L and T is a parabolic in nature and the
straight line. graph plotted between L and T is a

PROGEDURE
1. Determine the least count of Vernier Callipers and then measure the diameter of given bob.
2. Now tie the bob hook to the one end of thread and other end of thread pass through the split cork.
3. Hold the cork in clamp stand and placed it on the table.
4. Now set the length of pendulum at 25 cm from the centre of bob.
5. Take the bob towards left side at a distance of 4 cm to 5 cm from mean position and release it.
6. Count 20 oscillations and note the time for 20 oscillations by using stop watch.
7. Repeat the above steps for length of pendulum 50 cm, 75 cm, 100 cm, 125 cm and 150 cm from centre
of bob.
8. Plot the graph between L and T and L and T?
9. From graph determine length of second pendulum and acceleration due to gravity.

ORSEPVATIONS
Least count of Vernier Callipers = Cm.
Zero error in Verni r Callipers = cm.
Zero correction in Vernier Callipers = cm.
Observed diameter of bob d, = cm.
cm.
cm.
Mean observed diameter ofbob (d cm.
Correct diameter of bob (g = d + C cm.

Radius ofbob (r)= 2 Cm

Least count of stop watch = S.
Observation table

S.No. Length of Time for 20 oscillations Time Period T?

Pendulum Meant
T20 20
in

L=l+r in cm in S inS in S in

3.
4.
5.
6
 CALCUIAT cm.

Length of second pendulum fromL-T graph =

cm/S2
line of L T' graph
-
=

Slope of straight
=47t x Slope of straight line
g 42
cm/s

RESULTThe
graph plotted between L and T is parabolic.line.
a
1.
2. The graph plotted between L and T is a straight cm.
T' graph is
The Length of second pendulum from L-
.

3.
4. Acceleration due to gravity g _cm/s2.

P R E C A U T I O N S

of pendulum is rigid.
1. The base of stand must be heavy so that the support
should be in one vertical plane.
2. The oscillation's amplitude should be small and
3. There should be no rotatory motion of bob.
should be used.
4. Strong, weightless and inextensible thread
5. The stop watch should be accurate.

sOURCES OFFRROR
1. The length of pendulum may not be accurate.
2. The stop watch may not be accurate.
3. The thread may not be inextensible.
4. The point of suspension may not be rigid.
5. The air may disturb the oscillations of pendulum.

NT: FOR FILLING OBSERVATIONS AND ORSERVATIONS TABLE

Observations Least count of Vernier Callipers = 0.01 cm
Zero error in Vernier Callipers (e) = 0.00 cm
Zero correction in Vernier Callipers (c) = 0.00 cm
Observed diameter of bob d = 1.22 cm
d= 1.20 cm
d 1.18 cm
Mean observed diameter of bob d = 1.20 cm
Correct diameter of bob d = do+C = 1.20 cm
L
Radius of bobr = m = 0.60 cm

Least count of stop watch = 0.2 S

Observation table

S.No. Length of Time for 20 oscillations Time Period T?

Pendulum t Mean t T in
20
I+r=L in em in sec in sec in sec in sec sec

1. 19.4+0.6=20 18.0 18.0 18.0 0.9 0.81

2. 39.4 +0.6=40 26.0 26.0 26.0 1.3 1.69
3. 59.4 +0.6 60 32.8 32.0 32.8 1.6 2.56
4. 79.4+0.6 = 80 36.0 36.0 36.0 1.8 3.24
5. 179.40.6 =100 40.0 40.0 40.0 2.0 4.00
6. 119.4 0.6 =120 44.0 44.0 44.0 2.2 4.84

24 LAXMI PHYSICS Lab Manual (Class-X

 G Graph plotted between L andT
Scale
Along X axis 1 cm = 0.3 sec
120t Along Y axis 1 cm =20 cm

100
80+

60

404

20

O 0.3 0.6 0.9 1.2 1.5 1.8 2.1 X2.4

T in Sec

Graph plotted between I and T

Scale
Along X axis 1 cm = 1S2
Along Y axis 1 cm = 20 cm

120t
Length of second pendulum =
100 cm
100 Slope of st. line AC =A
=

BC AT
80 AL9648 482
|AL
Slope 24 cm/S2
60t g 4T2 x slope
40t B AT g=4xk 24
g 948 cm/$2
20t

2 3 5 X
T in S2 5
RFSULT:
1. The graph plotted between L and T is a parabolic.
2. The graph plotted between L and
T2 is a straight line.
3. The length of second
pendulum from LT graph is 100 cm.
4. The acceleration due to gravity g =
948 cm/s2.