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A 1 m long meter-bridge wire has a non-uniform cross-section so that the rate of change of its resistance with length satisfies dR/dl proportional to 1/sqrt(l). Two equal resistances are placed in the two gaps, and the galvanometer shows no deflection when the jockey touches point P on the wire. Find the distance AP from end A.

1. 0.25 m
2. 0.3 m
3. 0.35 m
4. 0.2 m

Correct answer: 0.25 m

Solution

Integrating dR/dl proportional to 1/sqrt(l) gives R(l) proportional to sqrt(l); balance with equal arms requires the two wire segments to have equal resistance.

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