 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2004

Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v.$ The retarding viscous force acting on the spherical ball is
A
inversely proportional to both radius $R$ and velocity $v$
B
directly proportional to both radius $R$ and velocity $v$
C
directly proportional to $R$ but inversely proportional to $v$
D
inversely proportional to $R,$ but directly proportional to velocity $v$

Explanation

From Stoke's law,

viscous force acting on the ball falling into a viscous fluid

$F = 6\pi \eta Rv$

$\therefore$ $F \propto R$ and $F \propto v$

hence $F$ is directly proportional to radius & velocity.
2

AIEEE 2004

A wire fixed at the upper end stretches by length $l$ by applying a force $F.$ The work done in stretching is
A
$2Fl$
B
$Fl$
C
${F \over {2l}}$
D
${{Fl} \over 2}$

Explanation

Work done by constant force in displacing the object by a distance $\ell$.

= Potential energy stored

$= {1 \over 2} \times$ Stress $\times$ Strain $\times$ Volume

$= {1 \over 2} \times {F \over A} \times {l \over L} \times AL$

$= {1 \over 2}Fl$
3

AIEEE 2002

A cylinder of height $20$ $m$ is completely filled with water. The velocity of efflux of water (in $m{s^{ - 1}}$) through a small hole on the side wall of the cylinder near its bottom is
A
$10$
B
$20$
C
$25.5$
D
$5$

Explanation

The velocity of efflux of water is given $v = \sqrt {2gh}$

Here $h$ is the height of the free surface of water from the hole

$\therefore$ $v = \sqrt {2 \times 10 \times 20} = 20m/s$