 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

A mass $'m'$ moves with a velocity $'v'$ and collides inelastically with another identical mass. After collision the ${1^{st}}$ mass moves with velocity ${v \over {\sqrt 3 }}$ in a direction perpendicular to the initial direction of motion. Find the speed of the ${2^{nd}}$ mass after collision. A
${\sqrt 3 v}$
B
$v$
C
${v \over {\sqrt 3 }}$
D
${2 \over {\sqrt 3 }}v$

Explanation

Assume speed of second mass = ${v_1}$

As momentum is conserved,

In $x$-direction, $mv = m{v_1}\cos \theta \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,....(1)$

In $y$-direction, ${{mv} \over {\sqrt 3 }} = m{v_1}\,\sin \theta \,\,\,\,\,\,\,\,\,\,...(2)$ Squaring and adding eqns.$(1)$ and $(2)$

${\left( {m{v_1}\cos \theta } \right)^2} + {\left( {m{v_1}\sin \theta } \right)^2}$$= {\left( {mv} \right)^2} + {\left( {{{mv} \over {\sqrt 3 }}} \right)^2}$

$\Rightarrow$ $v_1^2 = {v^2} + {{{v^2}} \over {\sqrt 3 }}$

$\Rightarrow {v_1} = {2 \over {\sqrt 3 }}v$

2

AIEEE 2004

A machine gun fires a bullet of mass $40$ $g$ with a velocity $1200m{s^{ - 1}}.$ The man holding it can exert a maximum force of $144$ $N$ on the gun. How many bullets can he fire per second at the most?
A
Two
B
Four
C
One
D
Three

Explanation

Assume the man can fire $n$ bullets in one second.

$\therefore$ change in momentum per second $= n \times mv = F$

[ $m=$ mass of bullet, $v=$ velocity, $F$ = force) ]

$\therefore$ $n = {F \over {mv}} = {{144 \times 1000} \over {40 \times 1200}} = 3$