phhysics investigatory project.pdf

physics investigatory project for class 12

1. INDEX
Contents
AIM....................................................................................................................2
INTRODUCTION..................................................................................................3
THEORY..............................................................................................................5
DIAGRAM............................................................................................................6
APPARATUS...........................................................................................................8
PROCEDURE.......................................................................................................9
OBSERVATION....................................................................................................11
CALCULATIONS...................................................................................................14
GRAPH...............................................................................................................17
RESULT….............................................................................................................18
PRECAUTIONS....................................................................................................19
SOURCES OF ERROR...........................................................................................20
BIBLIOGRAPHY .................................................................................................21

2. AIM:-
Using a simple pendulum, plot a L-T square graph, find
effective length of seconds pendulum.

3. INTRODUCTION :-
•A pendulum is an object, hung from a fixed point, that swings freely back
and forth under the action of gravity. A playground swing is an example of a
pendulum. The swing is supported by chains that are attached to fixed points
at the top of the swing set. When the swing is raised and released, it will
move freely back and forth. These back-and-forth movements are called
oscillations. The swing is moving due to the force of gravity on the swing.
The swing continues moving back and forth until friction (between the air
and the swing, and between the chains and the attachment points) slows it
down and eventually stops it.

4. •We see pendulums in other areas of our lives as well, such as in long-case
clocks, commonly known as grandfather clocks. But pendulums can do more
than entertain and help us tell time. Among other applications, they can show
that the Earth is rotating! This was done in the mid-1800s C.E. using perhaps
the most famous pendulum, Foucault's pendulum. However, pendulums were
being used for centuries before this. One of the first known pendulum uses
was around 100 C.E., when a Chinese scientist, Zhang Heng, used it to detect
distant earthquakes in a device called a seismometer. Today, pendulums have
many applications, including measuring local gravity and helping guide ships
and aircrafts.

5. THEORY :-
•A simple pendulum consists of a heavy metallic (brass) sphere with a hook (bob) suspended
from a rigid stand, with clamp by a weightless inextensible and perfectly flexible thread
through a slit cork, capable of oscillating in a single plane, without any friction, with a small
amplitude (less than 150) as shown in figure. There is no ideal simple pendulum. In practice,
we make a simple pendulum by tying a metallic spherical bob to a fine cotton stitching
thread.
• The spherical bob may be regarded by as a point mass at its center G. The distance
between the point of suspension S and the center G of the spherical bob is to be regarded as
the effective length of the pendulum as shown in figure. The effective length of a simple
pendulum, L = l + h + r. Where l is the length of the thread, h is length of hook, r is radius of
bob.

7. •The simple pendulum produces Simple Harmonic Motion (SHM) as the acceleration of
the pendulum bob is directly proportional to its displacement from the mean position and
is always directed towards it. The time period (T) of a simple pendulum for oscillations of
small amplitude, is given by the relation,
•T = 2 π√(L/g)
•Where, g = value of acceleration due to gravity and L is the effective length of the
pendulum.
•T2 = (4π2/g) X L or T2 = KL (K= constant) and, g = 4π2(L/T2)
•If T is plotted along the Y-axis and L along the X-axis, we should get a parabola. If T2 is
plotted along the Y-axis and L along the X-axis, we should get a straight line passing
through the origin.

8. APPARATUS :-
•A Clamp With Stand
•Bob with Hook
•Split Cork
•Stop Clock/Stopwatch
•Vernier Calipers
•Cotton Thread
•Half Meter Scale

9. PROCEDURE :-
•Find the vernier constant and zero error of the vernier callipers same as experiment 1.
•Measure the radius (r) of the bob using a vernier callipers same as experiment 1.
•Measure the length of hook (h) and note it on the table 6.1.
•Since h and r is already known, adjust the length of the thread l to make L = l + h + r an integer (say L = 80cm) and mark
it as M1 with ink. Making L an integer will make the drawing easier. (You can measure the distance between the point of
suspension (ink mark) and the point of contact between the hook and the bob directly. Hence you get l + h directly).
•Similarly mark M2, M3, M4 , M5, and M6 on the thread as distance (L) of 90 cm, 100 cm, 110cm, 120cm and 130 cm
respectively.
•Pass the thread through the two half-pieces of a split cork coming out just from the ink mark (M1).
•Tight the split cork between the clamp such that the line of separation of the two pieces of the split cork is at right angles
to the line along which the pendulum oscillates.
•Fix the clamp in the stand and place it on the table such that the bob is hanging at-least 2 cm above the base of the stand.

10. •Mark a point Aon the table (use a chalk) just below the position of bob at rest and draw a straight-line BC
of 10 cm having a point A at its center. Over this line bob will oscillate.
•Find the least count and the zero error of the stop clock/watch. Bring its hands at zero position
•Move the bob by hand to over position B on the right of A and leave. See that the bob returns over line BC.
Make sure that bob is not spinning.
•Now counting oscillations, from the instant bob passes through its mean position L, where its velocity is
maximum. So, starting from L it traverses LL2, L2L, LL1, L1L hence, one oscillation is completed. We must
find time for 20 such oscillations.
•Now start the stopwatch at the instant the bob passes through the mean position A. Go on counting the
number of oscillations it completes. As soon as it completes 20 oscillations, stop the watch. Note the time t
for 20 oscillations in the table 6.1.
•Repeat the measurement at least 3 times for the same length.
•Now increase the length of the thread by 10 cm or 15 cm (M2) and measure the time t for this length as
explained from step 6 to 14.
•Repeat step 15 for at least 4 more different lengths.

11. OBSERVATION :-
•Vernier constant = 0.01 cm
•Zero error of Vernier capiller = (i) 0cm, (ii) 0cm, (iii) 0cm
•Mean error = 0 cm
•Mean zero corrected error, ±e = 0 cm

12. Diameter of the bob and length of hook
•Observe diameter of the bob:= (i) 2.2 cm, (ii) 2.3 cm, (iii) 2.2 cm
•Mean diameter of bob, d0 = 2.2 cm
•Mean corrected diameter of bob, d = d0 ±e = 2.2 cm
•Radius of the bob, r = d/2= 1.1 cm
•Length of the hook, h= 1.7 cm
•Standard value acceleration due to gravity, g1 : 980 cm s-2
•Least count of stop clock = 0.01 s
•Zero error of stop clock = 0.00 s

13. Table 6.1 Determination of time-periods for different lengths of the pendulum.
78.2
88.2
98.2
108.2
118.2
80
90
100
110
120
36.04
37.93
40.63
41.87
44.21
35.88
37.97
40.34
41.85
43.85
35.78
40.38
38.00
41.75
43.44
37.96
35.90
40.45
41.82
43.82
1.79
1.89
35.88
2.02
2.09
2.19
3.3
3.6
4.0
4.4
4.8

14. Calculation:
•For each length, wire mean of 20 vibrations:
•T=(t1+t2+t3)/3
•T=(36.04+35.88+35.78)/3=35.90=>t/20=35.90/20=1.795
•T=(37.93+37.97+38.00)/3=37.96=>t/20=37.96/20=1.895
•T=(40.63+40.34+40.38)/3=40.45=>t/20=40.45/20=2.025
•T=(41.87+41.85+41.75)/3=41. 82=>t/20=41.82/20=2.095
•T=(44.21+43.85+43.41)/3=43. 82=>t/20=43.82/20=2.191

15. •T²=(1.79) ²=3.26²
•T²=(1.89) ²=3.65²
•T²=(2.02) ²=4.05²
•T²=(2.09) ²=4.45²
•T²=(2.19) ²=4.85²

16. •Graph:
•L vs T2Graph
•Plot the graph between L and T2from the observations recorded in
the table 6.1. Take L along X-axis and T2along Y-axis. The L-T curve
is a straight line passing through the (0, 0) point. So, the origin of the
graph should be chosen (0, 0). As shown in the figure 6.3.

18. RESULT :-
•Experimental length = 100 cm
•Actual length = 99.4 cm
•Percentage error = 0.6/99.4 X 100 = 0.6 %

19. PREACAUTIONS :-
•The thread should be very light and strong.
•The point of suspension should be reasonably rigid.
•The pendulum should oscillate in the vertical plane without any spin motion.
•The floor of the laboratory should not have vibration, which may cause a deviation from the regular
oscillation of the pendulum.
•The amplitude of vibration should be small (less than 15) .
•The length of the pendulum should be as large as possible in the given situation.’
•Determination of time for 20 or more oscillations should be carefully taken and repeated for at least
three times.
•There must not be strong wind blowing during the experiment.

20. SOURCES OF ERROR : -
•The string may not be weightless and inextensible point of
suspension may not be rigid. The amplitude may not be small.
The bob may spin.
•The air currents may disturb vibrations. There may be an error
in counting. The stopwatch may be inaccurate. There may be
delay in starting and stopping the stopwatch.

21. BIBLIOGRAPHY :-
•www.google.com
•www.wikipedia.org
•www.physicsprojects.com
•Comprehensive practical book