A student fills two containers with water (density 1.0 g/cm”) and two with oil (density 0.8 g/cm), as shown in the diagrams. In which container is the pressure on the base the greatest? water (a) Figure (A) (b) Figure (B) (c) Figure (C) (d) Figure (D)
Answers
Answer:
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Answer:
Lets say depth of A, B, C and D are h
A
, h
B
, h
C
and h
D
, then we have
P
A
=P
o
+h
A
ρg
P
B
=P
o
+h
B
ρg
P
C
=P
o
+h
C
ρg
P
D
=P
o
+h
D
ρg
∵h
B
=h
D
⇒P
D
=P
B
⇒ option A is correct.
∵h
A
<h
B
=h
D
<h
C
⇒P
A
<P
B
=P
D
<P
C
⇒ option B is correct.
Since ABCD is a square, So we can have
h
D
=h
B
=
2
h
C
+h
A
⇒h
D
ρg=h
B
ρg=
2
h
C
+h
A
ρg
⇒P
o
+h
D
ρg=P
o
+h
B
ρg=P
o
+
2
h
C
+h
A
ρg
⇒P
D
=P
B
=
2
P
o
+
2
P
o
+
2
h
C
ρg+
2
h
A
ρg
⇒P
D
=P
B
=
2
P
o
+
2
h
C
ρg
+
2
P
o
+
2
h
A
ρg
⇒P
D
=P
B
=
2
(P
o
+h
C
ρg)+(P
o
+h
A
ρg)
⇒P
D
=P
B
=
2
P
C
+P
A
⇒ option D is correct.
Lets say option 'C' is also correct
⇒P
D
=P
B
=
2
P
C
+P
A
=
2
P
C
−P
A
⇒
2
P
C
+P
A
=
2
P
C
−P
A
⇒
2
P
C
+
2
P
A
=
2
P
C
−
2
P
A
⇒
2
P
A
=−
2
P
A
⇒P
A
=0, (this is not true) ⇒ option C is incorrect.
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