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1

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)
A player kicks a football with an initial speed of 25 ms$$-$$1 at an angle of 45$$^\circ$$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms$$-$$2)
A
hmax = 10 m

T = 2.5 s
B
hmax = 15.625 m

T = 3.54 s
C
hmax = 15.625 m

T = 1.77 s
D
hmax = 3.54 m

T = 0.125 s

Explanation

$$H = {{{U^2}{{\sin }^2}\theta } \over {2g}}$$

$$ = {{{{(25)}^2}.{{(\sin 45)}^2}} \over {2 \times 10}}$$

= 15.625 m

$$T = {{U\sin \theta } \over g}$$

$$ = {{25 \times \sin 45^\circ } \over {10}}$$

= 2.5 $$\times$$ 0.7

= 1.77 s
2

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)
Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.
A
4.18 m
B
2.94 m
C
2.45 m
D
7.35 m

Explanation


H = $${1 \over 2}$$gt2

$${{9.8 \times 2} \over {9.8}}$$ = t2

t = $$\sqrt 2 $$ sec

$$\Delta$$t : time interval between drops

h = $${1 \over 2}$$g($$\sqrt 2 $$ $$-$$ 2$$\Delta$$t)2

$$\Delta$$t = $${1 \over {\sqrt 2 }}$$

h = $${1 \over 2}$$g$${\left( {\sqrt 2 - {1 \over {\sqrt 2 }}} \right)^2} = {1 \over 2} \times 9.8 \times {1 \over 2} = {{9.8} \over 4} = 2.45$$ m

H $$-$$ h = 9.8 $$-$$ 2.45

= 7.35 m
3

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)
A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
A
hyperbola
B
parabola in the direction of motion of plane
C
straight line vertically down the plane
D
parabola in a direction opposite to the motion of plane

Explanation

Relative velocity of bomb w.r.t. observer in plane = 0.

Bomb will fall down vertically. So, it will move in straight line w.r.t. observer.
4

JEE Main 2021 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)
A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $${h \over 3}$$ in both the directions.
A
$${{\sqrt 2 - 1} \over {\sqrt 2 + 1}}$$
B
$${1 \over 3}$$
C
$${{\sqrt 3 - \sqrt 2 } \over {\sqrt 3 + \sqrt 2 }}$$
D
$${{\sqrt 3 - 1} \over {\sqrt 3 + 1}}$$

Explanation

$$u = \sqrt {2gh} $$

Now,

$$S = {h \over 3}$$

a = $$-$$g

$$S = ut + {1 \over 2}a{t^2}$$

$${h \over 3} = \sqrt {2gh} t + {1 \over 2}( - g){t^2}$$

$${t^2}\left( {{g \over 2}} \right) - \sqrt {2gh} t + {h \over 3} = 0$$

From quadratic equation

$${t_1},{t_2} = {{\sqrt {2gh} \pm \sqrt {2gh - {{4g} \over 2}{h \over 3}} } \over g}$$

$${{{t_1}} \over {{t_2}}} = {{\sqrt {2gh} - \sqrt {{{4gh} \over 3}} } \over {\sqrt {2gh} + \sqrt {{{4gh} \over 3}} }} = {{\sqrt 3 - \sqrt 2 } \over {\sqrt 3 + \sqrt 2 }}$$

Questions Asked from Motion

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2022 (Online) 24th June Morning Shift [ Memory Based ] (3)
JEE Main 2021 (Online) 1st September Evening Shift (1)
JEE Main 2021 (Online) 31st August Morning Shift (1)
JEE Main 2021 (Online) 27th August Evening Shift (2)
JEE Main 2021 (Online) 26th August Evening Shift (1)
JEE Main 2021 (Online) 27th July Morning Shift (1)
JEE Main 2021 (Online) 25th July Evening Shift (3)
JEE Main 2021 (Online) 25th July Morning Shift (1)
JEE Main 2021 (Online) 20th July Evening Shift (1)
JEE Main 2021 (Online) 20th July Morning Shift (1)
JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 18th March Morning Shift (1)
JEE Main 2021 (Online) 17th March Evening Shift (2)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Evening Shift (1)
JEE Main 2021 (Online) 16th March Morning Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (2)
JEE Main 2021 (Online) 25th February Evening Shift (1)
JEE Main 2021 (Online) 25th February Morning Shift (2)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Evening Slot (1)
JEE Main 2020 (Online) 5th September Evening Slot (2)
JEE Main 2020 (Online) 5th September Morning Slot (2)
JEE Main 2020 (Online) 4th September Morning Slot (2)
JEE Main 2020 (Online) 3rd September Evening Slot (1)
JEE Main 2020 (Online) 2nd September Morning Slot (1)
JEE Main 2020 (Online) 9th January Evening Slot (1)
JEE Main 2020 (Online) 8th January Evening Slot (1)
JEE Main 2019 (Online) 12th April Evening Slot (2)
JEE Main 2019 (Online) 12th April Morning Slot (2)
JEE Main 2019 (Online) 10th April Evening Slot (1)
JEE Main 2019 (Online) 10th April Morning Slot (1)
JEE Main 2019 (Online) 9th April Evening Slot (2)
JEE Main 2019 (Online) 9th April Morning Slot (1)
JEE Main 2019 (Online) 8th April Evening Slot (2)
JEE Main 2019 (Online) 8th April Morning Slot (1)
JEE Main 2019 (Online) 12th January Morning Slot (2)
JEE Main 2019 (Online) 11th January Evening Slot (1)
JEE Main 2019 (Online) 11th January Morning Slot (1)
JEE Main 2019 (Online) 10th January Evening Slot (2)
JEE Main 2019 (Online) 10th January Morning Slot (2)
JEE Main 2019 (Online) 9th January Evening Slot (2)
JEE Main 2019 (Online) 9th January Morning Slot (1)
JEE Main 2018 (Online) 16th April Morning Slot (1)
JEE Main 2018 (Offline) (1)
JEE Main 2018 (Online) 15th April Evening Slot (1)
JEE Main 2018 (Online) 15th April Morning Slot (2)
JEE Main 2017 (Online) 9th April Morning Slot (1)
JEE Main 2017 (Online) 8th April Morning Slot (1)
JEE Main 2017 (Offline) (1)
JEE Main 2015 (Offline) (1)
JEE Main 2014 (Offline) (1)
JEE Main 2013 (Offline) (1)
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AIEEE 2011 (2)
AIEEE 2010 (4)
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