question_answer

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that the variation \[\frac{dR}{dl}\]of its resistance R with length l is \[\frac{dR}{dl}\propto \frac{1}{\sqrt{l}}.\] Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?                                                                                                [JEE Main 12-Jan-2019 Morning]

A)  0.35 m            

B)       0.2 m

C)  0.25 m

D)      0.3 m

Correct Answer: C

Solution :

          

[c] Let AP be the length

Taking integration on both the sides

Balancing point will divide the resistance in equal part. So, l will be correspond to .

or