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JEE Main 20179 AprilOnline

Exam: JEE Main
Year: 2017
Date: 9 April
Mode: Online
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2017 · 9 April · Online · Physics · Mechanical Properties of Fluids

Two tubes of radii r _ 1 and r _ 2 and lengths l _ 1 and l _ 2,...

Two tubes of radii

{r}_{1}

and

{r}_{2}

and lengths

{l}_{1}

and

{l}_{2,}

respectively, are connected in series and a liquid flows through each of them in stream line conditions.

{P}_{1}

and

{P}_{2}

are pressure differences across the two tubes. If

{P}_{2}

is

4{P}_{1}

and

{l}_{2}

is

\dfrac{{l}_{1}}{4}

then the radius

{r}_{2}

will be equal to :

Options

A $4{r}_{1}$
B ${r}_{1}$
C $2{r}_{1}$
D $\dfrac{{r}_{1}}{2}$

Correct answer

D. $\dfrac{{r}_{1}}{2}$

Step-by-step solution

\dfrac{dV}{dt} = \dfrac{\pi}{8}\dfrac{pr^{4}}{ηL}

\dfrac{{p}_{1}{r}_{1}^{4}}{{L}_{1}} = \dfrac{{p}_{2}{r}_{2}^{4}}{{L}_{2}}

\dfrac{{p}_{1}{r}_{1}^{4}}{l1} = 4{p}_{1}{r}_{2}^{4} \left(\dfrac{l1}{4}\right)<br /><br />

⇒{r}_{2}^{4} =

\dfrac{{r}_{1}^{4}}{16}<br /><br />

⇒{r}_{2} =

\dfrac{{r}_{1}}{2}

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