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JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)
A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $${1 \over 4}$$ times that of the bob and the length of the thread is increased by 1/3rd of the original length, then the time period of the simple harmonic oscillations will be :-
A
T
B
$${3 \over 2}$$T
C
$${3 \over 4}$$T
D
$${4 \over 3}$$T

Explanation

$$T = 2\pi \sqrt {l/g} $$

When bob is immersed in liquid

mgeff = mg $$-$$ Buoyant force

mgeff = mg $$-$$ v$$\sigma$$g ($$\sigma$$ = density of liquid)

$$ = mg - v{\rho \over 4}g$$

$$ = mg - {{mg} \over 4} = {{3mg} \over 4}$$

$$\therefore$$ $${g_{eff}} = {{3g} \over 4}$$

$${T_1} = 2\pi \sqrt {{{{l_1}} \over {{g_{eff}}}}} $$

$${l_1} = l + {l \over 3} = {{4l} \over 3},\,{l_{eff}} = {{3g} \over 4}$$

By solving

$${T_1} = {4 \over 3}2\pi \sqrt {l/g} $$

$${T_1} = {{4T} \over 3}$$
2

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $$\times$$ 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 $$\times$$ 1011 Pa, g = 9.8 m/s2]
A
3.60 $$\times$$ 10$$-$$8
B
2.60 $$\times$$ 10$$-$$7
C
1.87 $$\times$$ 10$$-$$3
D
7.07 $$\times$$ 10$$-$$4

Explanation

Force on each column = $${{mg} \over 4}$$

Strain = $${{mg} \over {4AY}}$$

$$ = {{50 \times {{10}^3} \times 9.8} \over {4 \times \pi (1 - 0.25) \times 2 \times {{10}^{11}}}}$$

= 2.6 $$\times$$ 10$$-$$7
3

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)
A uniform heavy rod of weight 10 kg ms$$-$$2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 $$\times$$ 1011 Nm$$-$$2. Neglecting the lateral contraction, find the elongation of rod due to its own weight.
A
2 $$\times$$ 10$$-$$9 m
B
5 $$\times$$ 10$$-$$8 m
C
4 $$\times$$ 10$$-$$8 m
D
5 $$\times$$ 10$$-$$10 m

Explanation


We know,

$$\Delta l = {{WL} \over {2AY}}$$

$$\Delta l = {{10 \times 1} \over {2 \times 5}} \times 100 \times {10^{ - 4}} \times 2 \times {10^{11}}$$

$$\Delta l = {1 \over 2} \times {10^{ - 9}} = 5 \times {10^{ - 10}}$$ m

Option (d)
4

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)
In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $$\times$$ 10$$-$$5 m and density 1.2 $$\times$$ 103 kgm$$-$$3 ? Take viscosity of liquid = 1.8 $$\times$$ 10$$-$$5 Nsm$$-$$2. (Neglect buoyancy due to air).
A
3.8 $$\times$$ 10$$-$$11 N
B
3.9 $$\times$$ 10$$-$$10 N
C
1.8 $$\times$$ 10$$-$$10 N
D
5.8 $$\times$$ 10$$-$$10 N

Explanation

Viscous force = Weight

$$ = \rho \times \left( {{4 \over 3}\pi {r^3}} \right)g$$

= 3.9 $$\times$$ 10$$-$$10

Questions Asked from Properties of Matter

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 31st August Evening Shift (2)
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