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Q.

Consider a shell rolling purely on a horizontal fixed surface.  The velocity of the centre of Shell is  v0i^  and acceleration of the centre of shell is  a0i^ .   
 Question Image
Following representative point are chosen on the shell 
P (on z-axis)
Q and R (on x-axis)
S (on y-axis)
Following symbolic representation has been used
r=  position vector of a point with respect to  o on ground
v =velocity vector of point with respect to ground 
ω=  angular velocity of the body
a=  acceleration of a point with respect to ground  
Match the conditions given in column-I with points given in column-II that obey the given condition at the instant shown.

 COLUMN -I COLUMN-II
ar.a=0pP
br.v=0qQ
cω.r=0rR
dα.r=0sS

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a

a-p,q,s;   b-p,q,r;   c-s;   d-p

b

a-p,q,s,;   b-p,q,s;   c-r,s;   d-q

c

a-p;   b-p,q,r,s;   c-q,r,s;   d-q,r,s

d

a-p,q,s;   b-p,q;   c-r;   d-p 

answer is C.

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Detailed Solution

 [ap;bp,q,r,s;cq,r,s]
 Question Image
 rs.as=ω2R.(2R) rp.aQ0,rR.aR0 rp.ap0
 Question Image 
v=ω×r

r.v=0

For any point
rp.ω0  see figure
For other   rpandω   are 1st

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