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Test Index
JEE Main 3 Apr 2025 Shift 1 Paper
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Section:
Physics
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© examsnet.com
Question : 31 of 75
Marks:
+1
,
-0
A piston of mass
M
M
M
is hung from a massless spring whose restoring force law goes as
F
=
−
k
x
3
F=-k x^3
F
=
−
k
x
3
, where
k
k
k
is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with '
n
n
n
' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature
T
T
T
) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height
L
0
L_0
L
0
to
L
1
L_1
L
1
, the total energy delivered by the filament is: (Assume spring to be in its natural length before heating)
[3 Apr 2025 Shift 1]
n
r
T
ln
(
L
1
L
0
)
+
M
g
(
L
1
−
L
0
)
+
k
4
(
L
1
4
−
L
0
4
)
n r T \ln \left( \frac{L_1}{L_0} \right) + M g (L_1 - L_0) + \frac{k}{4} (L_1^4 - L_0^4)
n
r
T
ln
(
L
0
L
1
)
+
M
g
(
L
1
−
L
0
)
+
4
k
(
L
1
4
−
L
0
4
)
3
n
r
T
ln
(
L
1
L
0
)
+
2
M
g
(
L
1
−
L
0
)
+
k
3
(
L
1
3
−
L
0
3
)
3 n r T \ln \left( \frac{L_1}{L_0} \right) + 2 M g (L_1 - L_0) + \frac{k}{3} (L_1^3 - L_0^3)
3
n
r
T
ln
(
L
0
L
1
)
+
2
M
g
(
L
1
−
L
0
)
+
3
k
(
L
1
3
−
L
0
3
)
n
r
T
ln
(
L
1
2
L
0
2
)
+
M
g
2
(
L
1
−
L
0
)
+
k
4
(
L
1
4
−
L
0
4
)
n r T \ln \left( \frac{L_1^2}{L_0^2} \right) + \frac{M g}{2} (L_1 - L_0) + \frac{k}{4} (L_1^4 - L_0^4)
n
r
T
ln
(
L
0
2
L
1
2
)
+
2
M
g
(
L
1
−
L
0
)
+
4
k
(
L
1
4
−
L
0
4
)
n
r
T
ln
(
L
1
L
0
)
+
M
g
(
L
1
−
L
0
)
+
3
k
4
(
L
1
4
−
L
0
4
)
n r T \ln \left( \frac{L_1}{L_0} \right) + M g (L_1 - L_0) + \frac{3k}{4} (L_1^4 - L_0^4)
n
r
T
ln
(
L
0
L
1
)
+
M
g
(
L
1
−
L
0
)
+
4
3
k
(
L
1
4
−
L
0
4
)
Validate
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