JEE Main 2014 · 9 Apr · Shift 1 · Physics Q10

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PhysicsSingle correct+4 / -1Question 10 of 90

A capillary tube is immersed vertically in water and the height of the water column is $x$ . When this arrangement is taken into a mine of depth $d$ , the height of the water column is $y$ . If $R$ is the radius of earth, the ratio $\dfrac xy$ is :

\left(1-\dfrac dR\right)

\left(1-\dfrac{2d}R\right)

\left(\dfrac{R-d}{R+d}\right)

\left(\dfrac{R+d}{R-d}\right)

Answer and worked solution

Official answer: A

The capillary rise $h=\dfrac{2T\cos\theta}{r\rho g}\propto\dfrac1g$ . At depth $d$ , $g'=g\left(1-\frac dR\right)$ , so
$\frac xy=\frac{g'}{g}=1-\frac dR.$

Topics:Capillarity Variation of g

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JEE Main 2014 · 9 Apr · Shift 1, Physics question 10