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JEE Advanced 2020 Full Test 2 Paper 1
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© examsnet.com
Question : 15
Total: 54
A piston weighing
W
=
3
kg has the form of a circular disc of radius
R
=
4
c
m
.
The disc has a hole into which a thin - walled pipe of radius
r
=
1
c
m
in inserted. Initially the piston is at the bottom of the cylinder. What height will the piston rise to if
m
=
700
g
of water is poured into the pipe?
Your Answer:
Validate
Solution:
Area of the piston
=
π
(
R
2
−
r
2
)
Pressure on the base
=
ρ
g
(
H
+
h
)
where
ρ
=
density of water.
Also pressure on the base
=
(
W
+
m
)
g
π
R
2
∴
ρ
g
(
H
+
h
)
=
(
W
+
m
)
g
π
R
2
⇒
H
+
h
(
W
+
m
)
π
R
2
ρ
...........(1)
Considering the equilibrium of the piston Upward thrust = weight of the piston
π
(
R
2
−
r
2
)
square
g
h
=
W
g
⇒
h
=
W
π
(
R
2
−
r
2
)
ρ
..............(2)
From (i) and (ii)
H
=
W
+
m
π
R
2
ρ
−
W
π
(
R
2
−
r
2
)
ρ
⇒
H
=
1
π
R
2
ρ
(
m
−
W
r
2
R
2
−
r
2
)
⇒
H
=
1
π
×
4
2
×
10
−
4
×
1000
=
(
0.7
−
3
×
1
2
×
10
−
4
(
4
2
−
1
2
)
×
10
−
4
)
=
10
c
m
© examsnet.com
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