 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2006

A player caught a cricket ball of mass $150$ $g$ moving at a rate of $20$ $m/s.$ If the catching process is completed in $0.1s,$ the force of the blow exerted by the ball on the hand of the player is equal to
A
$150$ $N$
B
$3$ $N$
C
$30$ $N$
D
$300$ $N$

Explanation

We know, Force$\times$ time = Impulse = Change in momentum

$\therefore$ $F \times t = m\left( {v - u} \right)$

$\Rightarrow$ $F = {{m\left( {v - u} \right)} \over t} = {{0.15\left( {0 - 20} \right)} \over {0.1}} = 30N$
2

AIEEE 2005

A block is kept on a frictionless inclined surface with angle of inclination $'\,\alpha \,'.$ The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to A
$g$ $cosec$ $\alpha$
B
$g/tan$ $\alpha$
C
$g$ $tan$ $\alpha$
D
$g$

Explanation

Acceleration of the block is to the right. Pseudo force acting on the block to the left. From diagram we can say,

m$a$cos$\alpha$ = m$g$sin$\alpha$

$\Rightarrow a = g\tan \alpha$
3

AIEEE 2005

Consider a car moving on a straight road with a speed of $100$ $m/s$. The distance at which car can be stopped is $\left[ {{\mu _k} = 0.5} \right]$
A
$1000$ $m$
B
$800$ $m$
C
$400$ $m$
D
$100$ $m$

Explanation

Acceleration due to friction = $\left( { - {\mu _k}g} \right)$

We know, ${v^2} = {u^2} + 2as$

$\Rightarrow$ ${0^2} = {u^2} + 2\left( { - {\mu _k}g} \right)s$

$\Rightarrow$ $2 { {\mu _k}g}s$ = ${u^2}$

$\Rightarrow s = {{{{100}^2}} \over {2 \times 0.5 \times 10}}$

$\Rightarrow s = 1000\,m$
4

AIEEE 2005

A particle of mass 0.3 kg subjected to a force $F=-kx$ with $k=15$ $N/m$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
A
$15\,\,\,\,m/{s^2}$
B
$3\,\,\,m/{s^2}$
C
$10\,\,\,m/{s^2}$
D
$5\,\,\,m/{s^2}$

Explanation

Given F = - kx

$\Rightarrow$ F = - 15$\times {{20} \over {100}}$ = - 3 N

F = m.a = 3 N

$\Rightarrow$ a = ${3 \over m}$ = ${3 \over {0.3}}$ = 10 m/s2