19. A gas bubble, from an explosion under water, oscillates with a period proportonal top the
static pressure, d the density of water and E the total energy of the explosion. The relation
between them is given below. Determine the values of a b and c
T is proportional to pred
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Answer:
T∝p
a
d
b
E
c
p→ML
−1
T
−2
d→ML
−3
E→ML
−2
T
−2
t∝(ML
−1
T
−2
)
a
(ML
−3
)
b
(ML
−2
T
−2
)
c
t∝M
a+b+c
L
a−3b+2c
T
−2a−2c
since, a+b+c=0
−a−3b+2c=0
a=3b+2c
∴(3b+2c)+b+c=0
4b+3c=0
⟹b=
4
−3c
−2a−2c=1
∴a=
2
−(1+2c)
So, −
2
1+22c
−
4
3c
+c=0
⟹c=
3
2
⟹a=
6
−7
⟹b=
2
−1
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