The period of oscillations of a simple pendulum is found to depend on its
length (l) and acceleration due to gravity (g) at a place. Obtain the relationship
among the physical quantities using dimensional analysis
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Explanation:
The period of oscillation of a simple pendulum is expected to depend upon the length of the pendulum (l), and acceleration due to gravity (g). The constant of proportionality is 2π. Then T =
A
g
2πl
B
2π
l
g
C
2π
g
l
D
l
2πg
Solution
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Correct option is
C
2π
g
l
T∝L
α
g
β
M
0
L
0
T
1
=L
α
(LT
−2
)
β
M
0
L
0
T
1
=L
α+β
T
−2β
⇒α+β=0,−2β=+1
⇒α=
2
1
,β=−
2
1
⇒T=2π
g
l
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