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JEE Main & Advanced JEE Main Paper (Held On 12-Jan-2019 Morning)

  • 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 Online Paper Held On 12-Jan-2019 Morning]

    A) 0.35 m                        

    B) 0.2 m

    C) 0.25 m            

    D)   0.3 m

    Correct Answer: C

    Solution :

    Let AP be the length \[l\] \[\frac{dR}{dl}\propto \frac{1}{\sqrt{l}},dR=K\frac{dl}{\sqrt{l}}\] Taking integration on both the sides \[\int_{{}}^{{}}{dR}=K\int_{{}}^{{}}{\frac{1}{\sqrt{l}}dl}\] \[R=2K{{l}^{1/2}}=2K\]                      \[(\because l=1m)\] Balancing point will divide the resistance in equal part. So, l will be correspond to \[K(\Omega )\].             \[\therefore \]\[K=2K\sqrt{l}\] or \[l=0.25m\]


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