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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

MCQ (Single Correct Answer)
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

MCQ (Single Correct Answer)
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) ]

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

Questions Asked from Impulse & Momentum

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
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