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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

MCQ (Single Correct Answer)
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
2

AIEEE 2005

MCQ (Single Correct Answer)
A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to slide is $$'n'$$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
A
$${\mu _k} = \sqrt {1 - {1 \over {{n^2}}}} $$
B
$${\mu _k} = 1 - {1 \over {{n^2}}}$$
C
$${\mu _k} = \sqrt {1 - {1 \over {{n^2}}}} $$
D
$${\mu _s} = 1 - {1 \over {{n^2}}}$$

Explanation


For smooth surface,

$$d = {1 \over 2}\left( {g\,\sin \,\theta } \right)t_1^2,$$

$${t_1} = \sqrt {{{2d} \over {g\,\sin \,\theta }}} ,$$


When surface is rough

$$d = {1 \over 2}\left( {g\,\sin \,\theta - \mu g\,\cos \theta } \right)t_2^2$$

$${t_2} = \sqrt {{{2d} \over {g\,\sin \,\theta - \mu g\,\cos \theta }}} $$

According to question, $${t_2} = n{t_1}$$

$$n\sqrt {{{2d} \over {g\,\sin \,\theta }}} = \sqrt {{{2d} \over {g\,\sin \,\theta - \mu g\,\cos \theta }}} $$

$$n = {1 \over {\sqrt {1 - {\mu _k}} }}$$ ( as $$\cos \,{45^ \circ } = \sin \,{45^ \circ } = {1 \over {\sqrt 2 }}$$ )

$${n^2} = {1 \over {1 - {\mu _k}}}$$

or $$1 - {\mu _k} = {1 \over {{n^2}}}$$

or $${\mu _k} = 1 - {1 \over {{n^2}}}$$

3

AIEEE 2005

MCQ (Single Correct Answer)
A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parachute opens, it decelerates at $$2\,\,m/{s^2}.$$ He reaches the ground with a speed of $$3$$ $$m/s$$. At what height, did he bail out?
A
$$182$$ $$m$$
B
$$91$$ $$m$$
C
$$111$$ $$m$$
D
$$293$$ $$m$$

Explanation


The velocity of parachutist when parachute opens at 50 m is

$$u = \sqrt {2gh} = \sqrt {2 \times 9.8 \times 50} = \sqrt {980} $$

The velocity at ground, $$v=3m/s$$

$$\therefore$$ $$S = {{{v^2} - {u^2}} \over {2 \times \left( { - 2} \right)}} = {{{3^2} - 980} \over { - 4}} \approx 243\,m$$

Initially he has fallen $$50$$ $$m.$$

$$\therefore$$ Total height from where

He bailed out $$=243+50=293m$$
4

AIEEE 2004

MCQ (Single Correct Answer)
A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of static friction between the block and the plane is $$0.8.$$ If the frictionless force on the block is $$10$$ $$N,$$ the mass of the block (in $$kg$$) is $$\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)$$
A
$$1.6$$
B
$$4.0$$
C
$$2.0$$
D
$$2.5$$

Explanation


For equilibrum of block,

$$mg\,\,\sin \theta = {f_s}\,\,$$

$$ \Rightarrow m \times 10 \times \sin {30^ \circ } = 10$$

$$ \Rightarrow m \times 5 = 10$$

$$ \Rightarrow m = 2.0\,\,kg$$

Questions Asked from Laws of Motion

On those following papers in MCQ (Single Correct Answer)
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