1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Evening Slot

The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 $$ \times $$ 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is
A
1.6 $$ \times $$ 103 km
B
3.2 $$ \times $$ 103 km
C
6.4 $$ \times $$ 103 km
D
1.28 $$ \times $$ 104 km

Explanation

Energy required to move a satellite from earth surface to height h is,

E1 = Uh $$-$$ Usurface

= $$-$$ $${{GMm} \over {R + h}} - \left( { - {{GMm} \over R}} \right)$$

= GMm $$\left( {{1 \over R} - {1 \over {R + h}}} \right)$$

= $${{GMm} \over {R(R + h)}} \times h$$

We know, for sattelite at height h.

Centrifigual force = Gravitational force

$$ \Rightarrow $$  $${{m{v^2}} \over {R + h}} = {{GMm} \over {{{\left( {R + h} \right)}^2}}}$$

$$ \Rightarrow $$  $$mv$$2 = $${{GMm} \over {R + h}}$$

$$ \therefore $$   $${1 \over 2}m{v^2}$$ = $${{GMm} \over {2\left( {R + h} \right)}}$$

$$ \therefore $$  Kinetic energy (E2) = $${{GMm} \over {2(R + h)}}$$

Given that,

E1 = E2

$$ \therefore $$  $${{GMm} \over {R(R + h)}} \times h = {{GMm} \over {2\left( {R + h} \right)}}$$

$$ \Rightarrow $$  $${h \over R} = {1 \over 2}$$

$$ \Rightarrow $$  h = $${R \over 2}$$

$$ \therefore $$  h = $${{6.4 \times {{10}^3}} \over 2}$$

= 3.2 $$ \times $$ 103 km
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Morning Slot

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -
A
mv2
B
$${1 \over 2}$$ mv2
C
$${3 \over 2}$$ mv2
D
2 mv2

Explanation

At height r from center of earth. orbital velocity

= $$\sqrt {{{GM} \over r}} $$

$$ \therefore $$  By energy conservation

KE of 'm' + $$\left( { - {{GMm} \over r}} \right)$$ = 0 + 0

(At infinity, PE = KE = 0)

$$ \Rightarrow $$  KE of 'm' = $${{{GMm} \over r}}$$ = $${\left( {\sqrt {{{GM} \over r}} } \right)^2}$$ m = mv2
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Evening Slot

Two stars of masses 3 $$ \times $$ 1031 kg each, and at distance 2 $$ \times $$ 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is - (Take Gravitational constant; G = 6.67 $$ \times $$ 10–11 Nm2 kg–2)
A
2.4 $$ \times $$ 104 m/s
B
1.4 $$ \times $$ 105 m/s
C
3.8 $$ \times $$ 104 m/s
D
2.8 $$ \times $$ 105 m/s

Explanation

By energy convervation between 0 & $$\infty $$.

$$ - {{GMm} \over r} + {{ - GMm} \over r} + {1 \over 2}m{V^2} = 0 + 0$$

[M is mass of star m is mass of meteroite)

$$ \Rightarrow $$ v $$ = \sqrt {{{4GM} \over r}} = 2.8 \times {10^5}$$m/s
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Morning Slot

A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :
A
$$\sqrt {gR} \left( {\sqrt 2 - 1} \right)$$
B
$$\sqrt {2gR} $$
C
$$\sqrt {gR} $$
D
$${{\sqrt {gR} } \over 2}$$

Explanation

v0 = $$\sqrt {g(R + h)} \approx \sqrt {gR} $$

ve = $$\sqrt {2g(R + h)} \approx \sqrt {2gR} $$

$$\Delta $$v=ve $$-$$ v0 = $$\left( {\sqrt 2 - 1} \right)\sqrt {gR} $$

Questions Asked from Gravitation

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2002 (4)
keyboard_arrow_right
AIEEE 2003 (3)
keyboard_arrow_right
AIEEE 2004 (4)
keyboard_arrow_right
AIEEE 2005 (3)
keyboard_arrow_right
AIEEE 2008 (2)
keyboard_arrow_right
AIEEE 2009 (1)
keyboard_arrow_right
AIEEE 2011 (1)
keyboard_arrow_right
AIEEE 2012 (2)
keyboard_arrow_right
JEE Main 2013 (Offline) (1)
keyboard_arrow_right
JEE Main 2014 (Offline) (1)
keyboard_arrow_right
JEE Main 2015 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2016 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Offline) (1)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2018 (Offline) (2)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Morning Slot (3)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Morning Slot (3)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Morning Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 22th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Evening Shift (1)
keyboard_arrow_right

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

Medical

NEET