A particle of mass m approaches a region of force starting from r = + ∞ The potential energy function in terms of distance r from the origin is given by,
U (r) = 
(3 a 2 - r 2 ) for, 0 
r 
a
= K/r for, r 
a
K > 0 (positive constant)
A
Derive the force F (r) and determine whether it is repulsive or attractive.
B
With what velocity should the particle start at r = ∞ to cross over to other side of the origin
C
If the velocity of the particle at r = ∞ is 
towards the origin describe the motion.
towards the origin describe the motion.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
repulsive
v > 
stops at r = a & then reaches to r = ∞ . r = a
Sol. 
= 
(–2r) ⇒ F(r) = 
r
= 
for 0 ≤ r ≤ a
= 
for r 
a
∴ K > 0
∴ force is +ve
∴ force is repulsive Ans.
m u 2 + 0 = 0 + 
u 2 = 
⇒ u = 
Ans.
m 
+ 0 = 0 + P.E. ⇒ P.E = 
⇒ r = a Ans.
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