1
MCQ (Single Correct Answer)

JEE Main 2021 (Online) 1st September Evening Shift

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

A
$${1 \over 2}\sqrt {{{GM} \over {R(2\sqrt 2 + 1)}}} $$
B
$${1 \over 2}\sqrt {{{GM} \over R}(2\sqrt 2 + 1)} $$
C
$${1 \over 2}\sqrt {{{GM} \over R}(2\sqrt 2 - 1)} $$
D
$$\sqrt {{{GM} \over R}} $$

Explanation


$${F_{net}} = {{M{V^2}} \over R}$$

$$\sqrt 2 F + {F_1} = {{M{V^2}} \over R}$$

$$\sqrt 2 {{GMM} \over {{{\left( {\sqrt 2 R} \right)}^2}}} + {{GMM} \over {{{(2R)}^2}}} = {{M{V^2}} \over R}$$

$${{GM} \over R}\left( {{1 \over {\sqrt 2 }} + {1 \over 4}} \right) = {V^2}$$

$${{GM} \over R}\left( {{{4 + \sqrt 2 } \over {4\sqrt 2 }}} \right) = {V^2}$$

$$V = \sqrt {{{GM\left( {4 + \sqrt 2 } \right)} \over {R4\sqrt 2 }}} $$

$$V = {1 \over 2}\sqrt {{{GM\left( {2\sqrt 2 + 1} \right)} \over R}} $$

Option (b)
2
MCQ (Single Correct Answer)

JEE Main 2021 (Online) 31st August Evening Shift

If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given : r < RE)
A
$$1 - {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} - {{{r^3}} \over {R_E^3}}$$
B
$$1 + {r \over {{R_E}}} + {{{r^2}} \over {R_E^2}} + {{{r^3}} \over {R_E^3}}$$
C
$$1 + {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} + {{{r^3}} \over {R_E^3}}$$
D
$$1 + {r \over {{R_E}}} - {{{r^2}} \over {R_E^2}} - {{{r^3}} \over {R_E^3}}$$

Explanation

$${g_{up}} = {g \over {{{\left( {1 + {r \over R}} \right)}^2}}}$$

$${g_{down}} = g\left( {1 - {r \over R}} \right)$$

$${{{g_{down}}} \over {{g_{up}}}} = \left( {1 - {r \over R}} \right){\left( {1 + {r \over R}} \right)^2}$$

$$ = \left( {1 - {r \over R}} \right)\left( {1 + {{2r} \over R} + {{{r^2}} \over {{R^2}}}} \right)$$

$$ = 1 + {r \over R} - {{{r^2}} \over {{R^2}}} - {{{r^3}} \over {{R^3}}}$$
3
MCQ (Single Correct Answer)

JEE Main 2021 (Online) 31st August Morning Shift

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :
A
$$V = {1 \over 2}\sqrt {{{4G({M_1} + {M_2})} \over r}} $$
B
$$V = \sqrt {{{4G({M_1} + {M_2})} \over r}} $$
C
$$V = {1 \over 2}\sqrt {{{2G({M_1} + {M_2})} \over r}} $$
D
$$V = {{\sqrt {2G} ({M_1} + {M_2})} \over r}$$

Explanation


$${1 \over 2}m{V^2} - {{G{M_1}m} \over {r/2}} - {{G{M_2}m} \over {r/2}} = 0$$

$${1 \over 2}m{V^2} = {{2Gm} \over r}({M_1} + {M_2})$$

$$V = \sqrt {{{4G({M_1} + {M_2})} \over r}} $$

Option (b)
4
MCQ (Single Correct Answer)

JEE Main 2021 (Online) 27th August Evening Shift

A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :
A
$$-$$60 G
B
+2 G
C
$$-$$20 G
D
$$-$$4 G

Explanation


$${V_A} = \left[ { - {{G{M_1}} \over r} - {{G{M_2}} \over R}} \right]$$

$$ = \left[ { - {{50} \over {25}}G - {{100} \over {50}}G} \right]$$

$$ = - 4G$$

Questions Asked from Gravitation

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

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Medical

NEET

Graduate Aptitude Test in Engineering

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