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JEE Advanced 2018 Question Paper 1 with solutions for online practice
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© examsnet.com
Question : 1
Total: 54
The potential energy of a particle of mass m at a distance r from a fixed point O is given by
V
(
r
)
=
k
r
2
∕
2
.
where ݇k is a positive constant of appropriate dimensions.
This particle is moving in a circular orbit of radius R about the point O.
If
v
is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true?
v
=
√
k
2
m
R
v
=
√
k
m
R
L
=
√
m
k
R
2
L
=
√
m
k
2
R
2
Validate
Solution:
V
=
k
r
2
2
,
F
=
−
k
r
(towards centre)
[
F
=
−
d
V
d
r
]
At
r
=
R
,
k
R
=
m
v
2
R
(Centripetal force)
v
=
√
k
R
2
m
=
√
k
m
R
,
L
=
m
√
k
m
R
2
© examsnet.com
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