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Q.

In the diagram strings, springs and the pulley are light and ideal. The system is in equilibrium with the strings taut (T > 0), match the column. Masses are equal.

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Column -1 Column -2
(A)Just after string W breaks(P)aA=0
(B)Just after spring X breaks(Q)aB=0
(C)Just after string Y breaks(R)aC=0
(D)Just after spring Z breaks (S)aB=aC

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a

A-p,r,s; B-r,s ;C-p; D-p,s

b

A-q,r,s; B-s; C-p;  D-p,s

c

A-q,r,s; B-p; C-s; D-s 

d

A-q,r,s; B-s; C-p,r ; D-p,s

answer is A.

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Detailed Solution

Explanation of the Problem:

The system involves two springs and several strings, with masses equal. The task is to match the conditions after different strings or springs break.

Step-by-Step Solution:

  1. Understanding the System:
    • The system is in equilibrium with taut strings.
    • When a string or spring breaks, the equilibrium will be disturbed, and the accelerations of the blocks will change.
  2. What happens when a string or spring breaks?
    • String W breaks:
      • If string W breaks, block B becomes unbalanced and its acceleration will be zero (aA = 0).
    • Spring X breaks:
      • If spring X breaks, the forces on block B change, resulting in its acceleration becoming zero (aB = 0).
    • String Y breaks:
      • When string Y breaks, block C loses support and its acceleration will be zero (aC = 0).
    • Spring Z breaks:
      • If spring Z breaks, blocks B and C will experience equal accelerations (aB = aC).

Final Matching:

  • (A) Just after string W breaks → (Q) aB = 0
  • (B) Just after spring X breaks → (R) aC = 0
  • (C) Just after string Y breaks → (P) aA = 0
  • (D) Just after spring Z breaks → (S) aB = aC
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