A particle is thrown with speed 
on the smooth circular track from point P as shown. ABC is a semicircular path of radius 
in the vertical plane. If the path length PA is 
and the particle returns to point P, then –
A
B
C
the minimum value of x if particle returns to point P is 
D
the minimum value of x if particle returns to point P is 2 r
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b, d):
= u 2 – 2g ×2r
= u 2 – 4gr … (1)
x = 
…
(2)
or, x 2 = 
as, x = 3r
∴ 9r 2 = 
From equation
(1) u 2 – 4gr = 
gr
⇒ u 2 = 
gr or u = 
Also minimum value of v C is 
From equation (2) x min = 2r
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