A capillary tube is immersed… - JEE Main 2014 Physics PYQ

JEE Main 2014 — Physics Mechanics

2014mcqeasy

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 $\frac{ x⁡ }{ y⁡ }$ is :

Official previous-year question

Held on 9 Apr 2014 · Verified 6 Jul 2026.

Options

A
$( \frac{ \text{R } - \text{ d} }{ \text{R } + \text{ d} } )$
B
$( \frac{ \text{R } + \text{ d} }{ \text{R } - \text{ d} } )$
C
$( 1 - \frac{ 2 \text{d} }{ \text{R} } )$
D
$( 1 - \frac{ \text{d} }{ \text{R} } )$

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Solution

We know that

$\text{h} = \frac{ 2 \text{T cos} \theta }{ \rho \text{gr} }$

$\therefore \text{x} = \frac{ 2 \text{T} cos \theta }{ \rho \text{gr} }$

Now, value of g $_{eff}$ at depth 'd' is

${\text{g}}_{\text{eff}} = \text{g} ( 1 - \frac{ \text{d} }{ \text{R} } )$

$\therefore \text{y} = \frac{ 2 \text{T} cos \theta }{ \rho {\text{g}}_{\text{eff}} \cdot \text{r} }$

$\therefore \frac{ \text{x} }{ \text{y} } = \frac{ {\text{g}}_{\text{eff}} }{ \text{g} } = 1 - \frac{ \text{d} }{ \text{R} }$

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Options

$( \frac{ \text{R } - \text{ d} }{ \text{R } + \text{ d} } )$

$( \frac{ \text{R } + \text{ d} }{ \text{R } - \text{ d} } )$

$( 1 - \frac{ 2 \text{d} }{ \text{R} } )$

$( 1 - \frac{ \text{d} }{ \text{R} } )$

Solution

We know that

$\text{h} = \frac{ 2 \text{T cos} \theta }{ \rho \text{gr} }$

$\therefore \text{x} = \frac{ 2 \text{T} cos \theta }{ \rho \text{gr} }$

Now, value of g $_{eff}$ at depth 'd' is

${\text{g}}_{\text{eff}} = \text{g} ( 1 - \frac{ \text{d} }{ \text{R} } )$

$\therefore \text{y} = \frac{ 2 \text{T} cos \theta }{ \rho {\text{g}}_{\text{eff}} \cdot \text{r} }$

$\therefore \frac{ \text{x} }{ \text{y} } = \frac{ {\text{g}}_{\text{eff}} }{ \text{g} } = 1 - \frac{ \text{d} }{ \text{R} }$

Options

Did you get this right?

Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics