 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

If $S$ is stress and $Y$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is
A
${{{S^2}} \over {2Y}}$
B
$2{S^2}Y$
C
${S \over {2Y}}$
D
${{2Y} \over {{S^2}}}$

Explanation

Energy stored per unit volume of wire,

$E = {1 \over 2} \times \,stress\, \times \,strain$

$\therefore$ $E = {1 \over 2} \times \,stress\, \times \,{{stress} \over Y} = {1 \over 2}{{{S^2}} \over Y}$

[ As Young's modulus(Y) = ${{Stress} \over {Strain}}$

$\therefore$ Strain = ${{Stress} \over Y}$ ]
2

AIEEE 2004

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is
A
$Ec$
B
$2E/c$
C
$E/c$
D
$E/{c^2}$

Explanation

Momentum of photon $= {E \over c}$

Change in momentum $= {{2E} \over c}$

$=$ momentum transferred to the surface

(the photon will reflect with same magnitude of momentum in opposite direction)
3

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.
4

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.