 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

Consider the following two statements:
$A.$$\,\,\,\,\,\, Linear momentum of a system of particles is zero B.$$\,\,\,\,\,\,$ Kinetic energy of a system of particles is zero.
then
A
$A$ does not imply $B$ and $B$ does not imply $A$
B
$A$ implies $B$ but $B$ does not imply $A$
C
$A$ does not imply $B$ but $B$ implies $A$
D
$A$ implies $B$ and $B$ implies $A$

Explanation

Kinetic energy of a system of particle is zero this is possible only when the speed of each particles is zero. And if speed of each particle is zero, the linear momentum of the system of particle has to be zero.

Also the linear momentum of the system may be zero even when the particles are moving in different direction. This is because linear momentum is a vector quantity. In this case the kinetic energy of the system of particles will not be zero.

$\therefore$ $A$ does not implies $B$ but $B$ implies $A.$

2

AIEEE 2002

A spring of force constant $800$ $N/m$ has an extension of $5$ $cm.$ The work done in extending it from $5$ $cm$ to $15$ $cm$ is
A
$16J$
B
$8J$
C
$32J$
D
$24J$

Explanation

When we extend the spring by $dx$ then the work done

$dW = k\,x\,dx$

Applying integration both sides we get,

$\therefore$ $W = k\int\limits_{0.05}^{0.15} {x\,dx}$

$= {{800} \over 2}\left[ {{{\left( {0.15} \right)}^2} - {{\left( {0.05} \right)}^2}} \right]$

$= 8\,J$
3

AIEEE 2002

If a body looses half of its velocity on penetrating $3$ $cm$ in a wooden block, then how much will it penetrate more before coming to rest?
A
$1$ $cm$
B
$2$ $cm$
C
$3$ $cm$
D
$4$ $cm$

Explanation

We know the work energy theorem, $W = \Delta K = FS$

For first penetration, by applying work energy theorem we get,

${1 \over 2}m{v^2} - {1 \over 2}m{\left( {{v \over 2}} \right)^2} = F \times 3\,\,...(i)$

For second penetration, by applying work energy theorem we get,

${1 \over 2}m{\left( {{v \over 2}} \right)^2} - 0 = F \times S\,...(ii)$

On dividing $(ii)$ by $(i)$

${{1/4} \over {3/4}} = S/3$

$\therefore$ $S = 1\,cm$