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VITEEE 2013 Solved Paper
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© examsnet.com
Question : 12
Total: 120
If the potential energy of a gas molecule is U =
M
r
6
−
N
r
12
, M and N being positive constants, then the potential energy at equilibrium must be
0
N
M
2
/4
M
N
2
/4
M
2
/4N
Validate
Solution:
Given, U =
M
r
6
−
N
r
12
∴ F =
−
d
u
d
r
=
−
d
d
r
(
M
r
6
−
N
r
12
)
= -
(
−
6
M
r
7
+
12
N
r
13
)
=
(
6
M
r
7
−
12
N
r
13
)
For equilibrium position, F = 0
∴
6
M
R
7
=
12
N
r
13
or
r
6
=
2
N
M
Hence, U =
M
(
2
N
∕
M
)
−
N
(
2
N
∕
M
2
)
=
M
2
/4N
© examsnet.com
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