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Byju's Answer
Standard IX
Physics
Pressure Due to Liquid Column
Two immiscibl...
Question
Two immiscible liquids of densities
ρ
and
2
ρ
and thickness (heights)
h
and
2
h
, respectively, push a vertical plate. Find the total side thrust given by the liquids on the vertical plate.
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Solution
Let small force exerted be
d
F
=
p
.
b
.
d
h
Pressure
=
P
=
x
p
g
x
=
depth
Then total force exerted
=
∫
d
F
=
∫
h
0
x
p
g
b
.
d
x
+
∫
2
h
0
(
h
p
g
+
x
.2
p
g
)
b
.
d
x
=
b
.
p
.
g
[
x
2
2
]
h
0
+
[
h
p
g
b
x
]
2
h
0
+
2
p
g
b
[
x
2
2
]
2
h
0
=
b
.
p
.
g
[
h
2
2
+
2
h
2
+
4
h
2
]
=
b
.
p
.
g
[
h
2
+
4
h
2
+
8
h
2
2
]
F
=
13
2
b
p
g
h
2
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