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Bar pendulm - Keters pandulum

Keters pandulum
Course

Principles Of Computer Science

84 Documents
Students shared 84 documents in this course
Academic year: 2022/2023
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Chhatrapati Shahu Ji Maharaj University

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Acceleration due to gravity ‘g’ by Bar Pendulum

OBJECT: To determine the value of acceleration due to gravity and radius of gyration using bar pendulum. Apparatus used: Bar pendulum, stop watch and meter scale. Formula: A. The general formula of the time period for bar pendulum is given by following equation:

g

ll g

l l

k

T 12

2

22

+

π=

+

π=

2

2 2

21

2

T

L

T

)l(l g π =

+π

44

(1)

Where l : distance between C. and suspension point, L: distance between suspension and

oscillation points, l

k lllL

2 21 +=+= , g: acceleration due to gravity, T: time period.

B. The time period is minimum when l =±k, in this situation the equation (1) becomes as:

g

k Tmin

2

2 π=

or 2 min

2

T

k g

π

8

(2)

where, k : radius of gyration, Tmin: minimum time period. The value of ‘g’ can be calculated using equations (1) and (2). The values of L, T, k and Tmin are obtained using graph between T and L for bar pendulum which is shown in following figure.

From Figures (1) and (2), (a) L 1 =AC+CD, L 2 =EC+CB and L=(L 1 +L 2 )/2, T=time at C (b) k =(PQ+QR)/2 and Tmin= time at Q

C. The radius of gyration can be obtained with following formula

= llk 21 (3) Where l 1 =(AC+CE)/2, l 2 =(BC+CD)/

D.K

Procedure: (1) Place the knife-edges at the first hole of the bar. (2) Suspend the pendulum through rigid support with the knife-edge. (3) Oscillate the pendulum for small amplitude (θ=3~4 0 ). (4) Note the time taken for 20 oscillations and measure the distance of the hole from the C. of the bar. (5) Repeat the observations (2)-(4) for knife-edges at first half side holes of bar. (6) Repeat the process (1)-(5) for the second half side of the bar. (7) Plot the graph between T and L. Observations: 1. Least count of the stop watch = ..... sec 2. Least count of the meter scale =...... cm 3. Table for l and T S. No.

l (cm)

t (time taken for 20 oscillations)

T = t/

For first half side of the bar 1 45 2 40 3 35 4 30 5 25 6 20 7 15 8 10 9 5 For second half side of the bar 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - Calculations: from graph , L=(AD+EB)/2=...., T=.., k=PR/2=... Tmin=.. l 1 =(AC+CE)/2=...., l 2 =(BC+CD)/

  1. 2

2

T

L

g

π

4

1 2. 2

min

2

T

k g

π

8

2 3. 2

gg g 21

+

= 4. = llk 21

Results: The acceleration due to gravity (g) = ........./s 2 Radius of gyration (k) =........ (from calculation) =........ (from graph) Precautions: 1. The motion of the pendulum should be in a vertical plane. While taking the time, start taking observations after two oscillations to avoid any irregularity of motion. 2. The amplitude of oscillation should be small.

D.K

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Bar pendulm - Keters pandulum

Course: Principles Of Computer Science

84 Documents
Students shared 84 documents in this course

University: Chhatrapati Shahu Ji Maharaj University

Was this document helpful?
Acceleration due to gravity ‘g’ by Bar Pendulum
OBJECT: To determine the value of acceleration due to gravity and radius of gyration using bar
pendulum.
Apparatus used: Bar pendulum, stop watch and meter scale.
Formula:
A. The general formula of the time period for bar pendulum is given by following equation:
g
ll
g
l
l
k
T12
2
22 +
π=
+
π=
2
2
2
21
2
T
L
T
)l(l
gπ
=
+π
=4
4 (1)
Where l: distance between C.G. and suspension point, L: distance between suspension and
oscillation points, l
k
lllL
2
21 +=+= , g: acceleration due to gravity, T: time period.
B. The time period is minimum when l=±k, in this situation the equation (1) becomes as:
g
k
Tmin
2
2π=
or 2
min
2
T
k
gπ
=8 (2)
where, k: radius of gyration, Tmin: minimum time period.
The value of ‘g’ can be calculated using equations (1) and (2).
The values of L, T, k and Tmin are obtained using graph between T and L for bar pendulum which
is shown in following figure.
From Figures (1) and (2),
(a) L1=AC+CD, L2=EC+CB and L=(L1+L2)/2, T=time at C
(b) k =(PQ+QR)/2 and Tmin= time at Q
C. The radius of gyration can be obtained with following formula
21llk = (3)
Where l1=(AC+CE)/2, l2=(BC+CD)/2
D.K.Pandey

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