 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2004

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that $B$ but uncharged is brought in contact with $B,$ then brought in correct with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is
A
$F/8$
B
$3$ $F/4$
C
$F/4$
D
$3$ $F/8$

Explanation

$F \propto {{{Q_A}{Q_C}} \over {{x^2}}}$

$x$ is distance between the spheres. After first operation charge on $B$ is halved i.e ${Q \over 2}.$

and charge on third sphere becomes ${Q \over 2}.$ Now it is touched to $C$, charge then equally

distributes them selves to make potential same, hence charge on $C$ becomes

$\left( {Q + {Q \over 2}} \right){1 \over 2} = {{3Q} \over 4}.$

$\therefore$ ${F_{new}} \propto {{{Q_C}{Q_B}} \over {{x^2}}}$

$= {{\left( {{{3Q} \over 4}} \right)\left( {{Q \over 2}} \right)} \over {{x^2}}}$

$= {3 \over 8}{{{Q^2}} \over {{x^2}}}$

or, ${F_{new}} = {3 \over 8}F$
2

AIEEE 2003

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter the change in the resistance of the wire will be
A
$200\%$
B
$100\%$
C
$50\%$
D
$300\%$

Explanation

${R_f} = {n^2}{R_1}$

Here $n=2$ (length becomes twice)

$\therefore$ ${R_f} = 4{R_i}$

New resistance $=400$ of ${R_i}$

$\therefore$ Increase $= 300\%$
3

AIEEE 2003

Three charges $- {q_1}, + {q_2}$ and $- {q_3}$ are placed as shown in the figure. The $x$-component of the force on $- {q_1}$ is proportional to A
${{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}\cos \theta$
B
${{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\sin \theta$
C
${{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\cos \theta$
D
${{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}sin\theta$

Explanation Force on charge ${q_1}$ due to ${q_2}$ is ${F_{12}} = k{{{q_1}{q_2}} \over {{b^2}}}$

Force on charge ${q_1}$ due to ${q_3}$ is ${F_{13}} = k{{{q_1}{q_3}} \over {{a^2}}}$

The $X$-component of the force $\left( {{F_x}} \right)$ on

$q{}_1$ is ${F_{12}} + {F_{13}}$ $\sin \theta$

$\therefore$ ${F_x} = k{{{q_1}{q_2}} \over {{b^2}}} + k{{{q_1}{q_2}} \over {{a^2}}}\sin \theta$

$\therefore$ ${F_x} \propto {{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\sin \theta$
4

AIEEE 2003

The work done in placing a charge of $8 \times {10^{ - 18}}$ coulomb on a condenser of capacity $100$ micro-farad is
A
$16 \times {10^{ - 32}}\,\,joule$
B
$3.1 \times {10^{ - 26}}\,\,joule$
C
$4 \times {10^{ - 10}}\,\,joule$
D
$32 \times {10^{ - 32}}\,\,joule$

Explanation

The work done is stored as the potential energy. The potential energy stored in a capacitor is given by

$U = {1 \over 2}{{{Q^2}} \over C}$

$= {1 \over 2} \times {{{{\left( {8 \times {{10}^{ - 18}}} \right)}^2}} \over {100 \times {{10}^{ - 6}}}}$

$= 32 \times {10^{ - 32}}J$