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IIT JEE Advanced 2012 Paper 2
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© examsnet.com
Question : 4
Total: 60
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertical in water in half- submerged state. If
ρ
c
is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
more than half-filled if
ρ
c
is less than 0.5.
more than half-filled if
ρ
c
is more than 1.0.
half-filled if
ρ
c
is more than 0.5.
less than half-filled if
ρ
c
is less than 0.5.
Validate
Solution:
We have
V
m
+
V
a
+
V
w
2
ρ
w
g
=
V
m
ρ
c
ρ
w
g
+
V
w
ρ
w
g
where
V
w
is the volume occupied by water in the shell,
V
a
is the volume occupied by air in the shell and
V
m
is the volume of the material in the shell.
V
w
=
V
m
(
1
−
2
ρ
c
)
+
V
a
If
ρ
c
>
1
2
, we get
V
w
<
V
a
.
If
ρ
c
<
1
2
, we get
V
w
<
V
a
.
© examsnet.com
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