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AIEEE 2012 Solved Paper
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© examsnet.com
Question : 42
Total: 89
If a simple pendulum has significant amplitude (up to a factor of
1
e
of original ) only in the period between
t
=
0
s
to
t
=
τ
s
, then
τ
may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with
b
as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :
0.693
b
b
1
b
2
b
Validate
Solution:
The equation of motion for the pendulum, suffering retardation
I
α
=
−
m
g
(
ℓ
s
i
n
θ
)
−
m
b
v
(
ℓ
)
where
I
=
m
ℓ
2
and
α
=
d
2
θ
∕
dt
2
∴
d
2
θ
d
t
2
=
−
g
ℓ
tan
θ
+
b
v
ℓ
on solving we get
θ
=
θ
0
e
b
t
2
s
i
n
(
ω
t
+
φ
)
According to questions
θ
0
e
=
θ
0
e
−
b
r
2
∴
τ
=
2
b
© examsnet.com
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