The air bubble formed by explosion inside water perform oscillations with time period T
which depends on pressure (p), density (ρ) and on energy due to explosion (E).
Establish relation between T, p, E and ρ.
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23
Answer
T∝P
a
d
b
E
c
P=[M][L]
−1
[T]
−2
d=[M][L]
−3
E=[M][L]
2
[T]
−2
T=[M]
(a+b+c)
[L]
(−a−3b+2c)
[T]
(−2a−2c)
a+b+c=0
a+c=−b
−a−3b+2c=0
−2a−2c=1
2b=1
b=
2
1
a+c=−
2
1
and2c−a=3b=
2
3
3c=1
c=
3
1
anda=−
6
5
T=P
−
6
5
d
2
1
E
3
1
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