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JEE Main Physics Class 11 Oscillations Part 1 Questions
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© examsnet.com
Question : 64
Total: 100
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass
M
. The piston and the cylinder have equal cross sectional area
A
. When the piston is in equilibrium, the volume of the gas is
V
0
and its pressure is
P
0
. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[2013]
1
2
π
A
γ
P
0
V
0
M
1
2
π
V
0
M
P
0
A
2
γ
1
2
π
√
A
2
γ
P
0
M
V
0
1
2
π
√
M
V
0
A
γ
P
0
Validate
Solution:
M
g
A
=
P
0
P
0
V
0
γ
=
P
V
γ
M
g
=
P
0
A
.....(i)
Let piston is displaced by distance
x
P
0
A
x
0
γ
=
P
A
(
x
0
−
x
)
γ
P
=
P
0
x
0
γ
(
x
0
−
x
)
γ
M
g
−
(
P
0
x
0
γ
(
x
0
−
x
)
γ
)
A
=
F
restoring
P
0
A
(
1
−
x
0
γ
(
x
0
−
x
)
γ
)
=
F
restoring
[
x
0
−
x
≈
x
0
]
F
=
−
γ
P
0
A
x
x
0
∴
Frequency with which piston executes SHM.
f
=
1
2
π
√
γ
P
0
A
x
0
M
=
1
2
π
√
γ
P
0
A
2
M
V
0
© examsnet.com
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