### JEE Main 12 Jan 2019 Morning Question 19

##### Question: 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]

#### Options:

A) 0.35 m

B) 0.2 m

C) 0.25 m

D) 0.3 m

## Show Answer

#### Answer:

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 $