### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2004

If two soap bubbles of different radii are connected by a tube
A
air flows from the smaller bubble to the bigger
B
air flows from bigger bubble to the smaller bubble till the sizes are interchanged
C
air flows from the bigger bubble to the smaller bubble till the sizes become equal
D
there is no flow of air.

## Explanation

Pressure inside the bubble, P $= {p_0} + {{4T} \over R}$

So $P \propto {1 \over R}$ where R is the radius of the bubble. It means pressure inside a smaller bubble is greater than the inside of a bigger bubble.

So when two bubbles are connected by a tube, air will flow from smaller bubble to bigger bubble and the size of bigger bubble will increase.
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

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