The document discusses a physics problem related to work, energy, and power, specifically examining a particle's potential energy and its motion around a fixed point. It provides equations for the particle's potential energy, force, and angular momentum, determining that options (b) and (c) are correct. Additionally, it includes promotional links for a physics helpline and social media channels.

1. Physics Helpline
L K Satapathy Work Energy Power 4
JEE ADV 2018
[ One or more correct ]

2. Physics Helpline
L K Satapathy Work Energy Power 4
The potential energy of a particle of mass m at a distance r from a
fixed point O is given by , where K is a positive
constant of appropriate dimensions. The particle is moving in an
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 ?
2
( )
2
Kr
V r 
Question : JEE ADV 2018 [ 1 or more correct ]
2 2
( ) ( ) ( ) ( )
2 2
K K mK
a v R b v R c L mK R d L R
m m
   

3. Physics Helpline
L K Satapathy Work Energy Power 4
Answer :
Potential energy of the particle at distance r is
2
( )
2
Kr
V r 
 Force on the particle at a distance r is
2
2
2 2
dV d Kr K
F r Kr
dr dr
 
         
 
 Force on the particle at a distance R is F KR 
 Centripetal Force on the particle is
2
2 2mv K K
F KR v R v R
R m m
       (b) is correct
 Correct options = (b) , (c)
 Angular momentum
2K
L mvR mR R mK R
m
    (c) is correct

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L K Satapathy
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