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Q.

In x-y plane, there exist 2 circles  C1:(x1)2+(y2)2=4 and C2:(x5)2+(y2)2=4 . In the region, there exist two variable forces given by:
F¯1=k{(1y)i^+(x2)j^}  and  F¯2=k{(1y)i^+(x2)j^}(1y)2+(x2)2
Let  Wij  represent the work done by F¯i   in a complete rotation in anticlockwise direction for cyclic path along circle Cj . Match  Wij  in Column-I to its value in Column-II.
 

Column-I

Column-II

P)W111)2πk
Q)W122)4πk
R)W213)8πk
S)W224)16πk
  5)0

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a

P2,Q2;R1,S5

b

P3,Q3;R1,S5

c

P3,Q3;R5,S5

d

P3,Q3;R1,S1

answer is B.

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Detailed Solution

Taking origin of another coordinate system as (1,2)
 F¯1=krθ^;F¯2=krθ^ W1=kr2dθ2     W2=Kdθ
 
 
 

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In x-y plane, there exist 2 circles  C1:(x−1)2+(y−2)2=4 and C2:(x−5)2+(y−2)2=4 . In the region, there exist two variable forces given by:F¯1=k{(1−y)i^+(x−2)j^}  and  F¯2=k{(1−y)i^+(x−2)j^}(1−y)2+(x−2)2Let  Wij  represent the work done by F¯i   in a complete rotation in anticlockwise direction for cyclic path along circle Cj . Match  Wij  in Column-I to its value in Column-II. Column-IColumn-IIP)W111)2πkQ)W122)4πkR)W213)8πkS)W224)16πk  5)0