2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the
orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape
velocity from the planet is:
A.
2
B.
1
C.
$\sqrt 2 $
D.
${1 \over {\sqrt 2 }}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Morning Slot
On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by ${{Ax} \over {{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}}$ in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
A.
${A{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}$
B.
${A{{\left( {{x^2} + {a^2}} \right)}^{1/2}}}$
C.
${A \over {{{\left( {{x^2} + {a^2}} \right)}^{1/2}}}}$
D.
${A \over {{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
The mass density of a planet of radius R varies with the distance r from its centre as
$\rho $(r) = ${\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$.
Then the gravitational field is maximum at :
$\rho $(r) = ${\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$.
Then the gravitational field is maximum at :
A.
$r = {1 \over {\sqrt 3 }}R$
B.
r = R
C.
$r = \sqrt {{3 \over 4}} R$
D.
$r = \sqrt {{5 \over 9}} R$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to
that of the earth’s radius Re
. By firing rockets attached to it, its speed is instantaneously increased
in the direction of its motion so that it become $\sqrt {{3 \over 2}} $
times larger. Due to this the farthest distance
from the centre of the earth that the satellite reaches is R. Value of R is :
A.
2Re
B.
3Re
C.
4Re
D.
2.5Re
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Evening Slot
The height ‘h’ at which the weight of a body will
be the same as that at the same depth ‘h’ from
the surface of the earth is (Radius of the earth
is R and effect of the rotation of the earth is
neglected)
A.
${R \over 2}$
B.
${{\sqrt 5 R - R} \over 2}$
C.
${{\sqrt 3 R - R} \over 2}$
D.
${{\sqrt 5 } \over 2}R - R$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
The mass density of a spherical galaxy varies
as
${K \over r}$ over a large distance ‘r’ from its centre.
In that region, a small star is in a circular orbit
of radius R. Then the period of revolution, T
depends on R as :
A.
T2 $ \propto $ R
B.
T2 $ \propto $ R3
C.
T $ \propto $ R
D.
T2 $ \propto $ ${1 \over {{R^3}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Evening Slot
Planet A has mass M and radius R. Planet B has
half the mass and half the radius of Planet A.
If the escape velocities from the Planets A and
B are vA and vB, respectively, then ${{{v_A}} \over {{v_B}}} = {n \over 4}$.
The value of n is :
A.
1
B.
2
C.
4
D.
3
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
A body A of mass m is moving in a circular orbit
of radius R about a planet. Another body B of
mass
${m \over 2}$
collides with A with a velocity which is half $\left( {{{\overrightarrow v } \over 2}} \right)$ the instantaneous velocity${\overrightarrow v }$
of A.
The collision is completely inelastic. Then, the
combined body :
A.
starts moving in an elliptical orbit around
the planet.
B.
Falls vertically downwards towards the
planet
C.
Escapes from the Planet's Gravitational field.
D.
continues to move in a circular orbit
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Morning Slot
Consider two solid spheres of radii R1 = 1m,
R2 = 2m and masses M1 and M2, respectively.
The gravitational field due to sphere (1) and (2) are shown. The value of ${{{M_1}} \over {{M_2}}}$ is :
A.
${2 \over 3}$
B.
${1 \over 6}$
C.
${1 \over 2}$
D.
${1 \over 3}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Evening Slot
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same
balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius
of the earth = 6400 km) :
A.
194.32 N
B.
195.66 N
C.
195.32 N
D.
194.66 N
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket
of mass ${m \over {10}}$
so that subsequently the
satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
A.
${{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2}$
B.
${m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right)$
C.
$5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right)$
D.
${m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2}$
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 8th January Evening Slot
A ball is dropped from the top of a 100 m high
tower on a planet. In the last ${1 \over 2}s$ before hitting
the ground, it covers a distance of 19 m.
Acceleration due to gravity (in ms–2) near the
surface on that planet is _____.
Correct Answer: 8
Explanation:
Let time to travel 81 m is t sec.
Time to travel 100 m is t + ${1 \over 2}$ sec.
$ \therefore $ 81 = ${1 \over 2}$ $ \times $ a $ \times $ t2
$ \Rightarrow $ t = $9\sqrt {{2 \over a}} $
And 100 = ${1 \over 2}$ $ \times $ a $ \times $ ${\left( {{1 \over 2} + t} \right)^2}$
$ \Rightarrow $ $t + {1 \over 2}$ = $10\sqrt {{2 \over a}} $
$ \Rightarrow $ $9\sqrt {{2 \over a}} $ + ${1 \over 2}$ = $10\sqrt {{2 \over a}} $
$ \Rightarrow $ $\sqrt {{2 \over a}} $ = ${1 \over 2}$
$ \Rightarrow $ a = 8 m/s2
Time to travel 100 m is t + ${1 \over 2}$ sec.
$ \therefore $ 81 = ${1 \over 2}$ $ \times $ a $ \times $ t2
$ \Rightarrow $ t = $9\sqrt {{2 \over a}} $
And 100 = ${1 \over 2}$ $ \times $ a $ \times $ ${\left( {{1 \over 2} + t} \right)^2}$
$ \Rightarrow $ $t + {1 \over 2}$ = $10\sqrt {{2 \over a}} $
$ \Rightarrow $ $9\sqrt {{2 \over a}} $ + ${1 \over 2}$ = $10\sqrt {{2 \over a}} $
$ \Rightarrow $ $\sqrt {{2 \over a}} $ = ${1 \over 2}$
$ \Rightarrow $ a = 8 m/s2
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 8th January Evening Slot
An asteroid is moving directly towards the
centre of the earth. When at a distance of
10R (R is the radius of the earth) from the earths
centre, it has a speed of 12 km/s. Neglecting
the effect of earths atmosphere, what will be the
speed of the asteroid when it hits the surface
of the earth (escape velocity from the earth is
11.2 km/s) ? Give your answer to the nearest
integer in kilometer/s _____.
Correct Answer: 16
Explanation:
U1 + K1 = U2 + K2
$ \Rightarrow $ $ - {{GMm} \over {10R}} + {1 \over 2}mV_1^2$ = $ - {{GMm} \over R} + {1 \over 2}mV_2^2$
$ \Rightarrow $ ${1 \over 2}V_2^2 = {1 \over 2}V_1^2 + {{GM} \over R} - {{GM} \over {10R}}$
$ \Rightarrow $ $V_2^2 = V_1^2 + {9 \over 5}{{GM} \over R}$ ....(1)
Given escape velocity Ve = 11.2 km/s
$ \Rightarrow $ $\sqrt {{{2GM} \over R}} $ = 11.2
$ \Rightarrow $ ${{{GM} \over R} = {{{{\left( {11.2} \right)}^2}} \over 2}}$
So from (1)
$V_2^2 = V_1^2 + {9 \over 5}$${ \times {{{{\left( {11.2} \right)}^2}} \over 2}}$
= ${\left( {12} \right)^2}$ + 112.896
$ \Rightarrow $ V2 = 16 km/s
$ \Rightarrow $ $ - {{GMm} \over {10R}} + {1 \over 2}mV_1^2$ = $ - {{GMm} \over R} + {1 \over 2}mV_2^2$
$ \Rightarrow $ ${1 \over 2}V_2^2 = {1 \over 2}V_1^2 + {{GM} \over R} - {{GM} \over {10R}}$
$ \Rightarrow $ $V_2^2 = V_1^2 + {9 \over 5}{{GM} \over R}$ ....(1)
Given escape velocity Ve = 11.2 km/s
$ \Rightarrow $ $\sqrt {{{2GM} \over R}} $ = 11.2
$ \Rightarrow $ ${{{GM} \over R} = {{{{\left( {11.2} \right)}^2}} \over 2}}$
So from (1)
$V_2^2 = V_1^2 + {9 \over 5}$${ \times {{{{\left( {11.2} \right)}^2}} \over 2}}$
= ${\left( {12} \right)^2}$ + 112.896
$ \Rightarrow $ V2 = 16 km/s
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass
of the planet is
${1 \over 9}$
th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?
(Take the planets to have the same mass density)
A.
${R \over 9}$
B.
${R \over 2}$
C.
${R \over 3}$
D.
${R \over 4}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational
field of the planet acts on the spaceship, what will be the number of complete revolutions made by the
spaceship in 24 hours around the planet?
[Given ; Mass of planet = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2 /kg2]
[Given ; Mass of planet = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2 /kg2]
A.
13
B.
9
C.
17
D.
11
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
The value of acceleration due to gravity at
Earth's surface is 9.8 ms–2. The altitude above
its surface at which the acceleration due to
gravity decreases to 4.9 ms–2, is close to :
(Radius of earth = 6.4 × 106 m)
A.
1.6 × 106 m
B.
9.0 × 106 m
C.
6.4 × 106 m
D.
2.6 × 106 m
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
A test particle is moving in a circular orbit in
the gravitational field produced by a mass
density $\rho (r) = {K \over {{r^2}}}$ . Identify the correct relation
between the radius R of the particle's orbit and
its period T
A.
T2/R3 is a constant
B.
TR is a constant
C.
T/R2 is a constant
D.
T/R is a constant
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
A solid sphere of mass 'M' and radius 'a' is
surrounded by a uniform concentric spherical
shell of thickness 2a and mass 2M. The
gravitational field at distance '3a' from the
centre will be :
A.
${{GM} \over {3{a^2}}}$
B.
${{2GM} \over {9{a^2}}}$
C.
${{GM} \over {9{a^2}}}$
D.
${{2GM} \over {3{a^2}}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
A rocket has to be launched from earth in such
a way that it never returns. If E is the minimum
energy delivered by the rocket launcher, what
should be the minimum energy that the
launcher should have if the same rocket is to
be launched from the surface of the moon ?
Assume that the density of the earth and the
moon are equal and that the earth's volume is
64 times the volume of the moon :-
A.
E/32
B.
E/16
C.
E/4
D.
E/64
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
Four identical particles of mass M are located
at the corners of a square of side 'a'. What
should be their speed if each of them revolves
under the influence of other's gravitational field
in a circular orbit circumscribing the square?
A.
$1.21\sqrt {{{GM} \over a}} $
B.
$1.16\sqrt {{{GM} \over a}} $
C.
$1.41\sqrt {{{GM} \over a}} $
D.
$1.35\sqrt {{{GM} \over a}} $
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Evening Slot
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is ;
A.
2
B.
${{1 \over 2}}$
C.
$\sqrt {{1 \over 2}} $
D.
1
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2 , is given by :
A.
$Gm\left[ {A\left( {{1 \over a} - {1 \over {a + L}}} \right) - BL} \right]$
B.
$Gm\left[ {A\left( {{1 \over a} - {1 \over {a + L}}} \right) + BL} \right]$
C.
$Gm\left[ {A\left( {{1 \over {a + L}} - {1 \over a}} \right) + BL} \right]$
D.
$Gm\left[ {A\left( {{1 \over {a + L}} - {1 \over a}} \right) - BL} \right]$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Morning Slot
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :
A.
in the same circular orbit of radius R
B.
such that it escapes to infinity
C.
in a circular orbit of a different radius
D.
in an elliptical orbit
2019
JEE Mains
MCQ
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.
${{\sqrt {gR} } \over 2}$
2019
JEE Mains
MCQ
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
2019
JEE Mains
MCQ
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
2019
JEE Mains
MCQ
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
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 16th April Morning Slot
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :
A.
Weight of the object, everywhere on the earth, will increase.
B.
Weight of the object, everywhere on the earth, will decrease.
C.
There will be no change in weight anywhere on the earth.
D.
Except at poles, weight of the object on the earth will decrease.
2018
JEE Mains
MCQ
JEE Main 2018 (Offline)
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely
proportional to the nth power of R. If the period of rotation of the particle is T, then :
A.
T $ \propto $ Rn/2
B.
T $ \propto $ R3/2 for any n
C.
T $ \propto $ Rn/2 +1
D.
T $ \propto $ R(n+1)/2
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
Take the mean distance of the moon and the sun from the earth to be $0.4 \times {10^6}$ km and $150 \times {10^6}$ km respectively. Their masses are $8 \times {10^{22}}$ kg and $2 \times {10^{30}}$ kg respectively. The radius of the earth is $6400$ km. Let $\Delta {F_1}$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta {F_2}$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ${{\Delta {F_1}} \over {\Delta {F_2}}}$ is :
A.
$2$
B.
${10^{ - 2}}$
C.
$0.6$
D.
$6$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius ${R \over 2},$ and the other mass, in a circular orbit of radius ${3R \over 2}$. The difference between the final and initial total energies is :
A.
$ - {{GMm} \over {2R}}$
B.
$ + {{GMm} \over {6R}}$
C.
${{GMm} \over {2R}}$
D.
$ - {{GMm} \over {6R}}$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 9th April Morning Slot
The mass density of a spherical body is given by
$\rho $ (r) = ${k \over r}$ for r $ \le $ R and $\rho $ (r) = 0 for r > R,
where r is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :
$\rho $ (r) = ${k \over r}$ for r $ \le $ R and $\rho $ (r) = 0 for r > R,
where r is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :
A.
B.
C.
D.
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 8th April Morning Slot
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh ${3 \over 4}$ W. Radius of the Earth is 6400 km and g=10 m/s2.
A.
1.1 $ \times $ 10−3 rad/s
B.
0.83 $ \times $ 10−3 rad/s
C.
0.63 $ \times $ 10−3 rad/s
D.
0.28 $ \times $ 10−3 rad/s
2017
JEE Mains
MCQ
JEE Main 2017 (Offline)
The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by
(R = Earth’s radius):
A.
B.
C.
D.
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is ${1 \over 4}$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t1 is the time taken for planet to go over path abc and t2 for path taken over cda then :
A.
t1 = t2
B.
t1 = 2t2
C.
t1 = 3t2
D.
t1 = 4t2
2016
JEE Mains
MCQ
JEE Main 2016 (Offline)
A satellite is revolving in a circular orbit at a height $'h'$ from the earth's surface (radius of earth $R;h < < R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)
A.
$\sqrt{2 g R}$
B.
$\sqrt{g R}$
C.
$\sqrt{g R / 2}$
D.
$\sqrt{g R}(\sqrt{2}-1)$
2016
JEE Mains
MSQ
JEE Main 2016 (Online) 10th April Morning Slot
An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is :
A.
Zero since astronaut feels weightless
B.
0 < FG < ${{GMm} \over {{R^2}}}$
C.
${{GMm} \over {{{\left( {R + h} \right)}^2}}}$ < FG < ${{GMm} \over {{R^2}}}$
D.
FG = ${{GMm} \over {{{\left( {R + h} \right)}^2}}}$
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R/2$ is removed, as shown in the figure. Taking gravitational potential $V=0$ at $r = \infty ,$ the potential at the center of the cavity thus formed is:
($G=gravitational $ $constant$)
($G=gravitational $ $constant$)
A.
${{ - 2GM} \over {3R}}$
B.
${{ - 2GM} \over R}$
C.
${{ - GM} \over {2R}}$
D.
${{ - GM} \over R}$
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is :
A.
$\sqrt {{{GM} \over R}} $
B.
$\sqrt {2\sqrt 2 {{GM} \over R}} $
C.
$\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)} $
D.
${1 \over 2}\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)} $
All those particles are moving due to their mutual gravitational attraction.
2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$?
A.
${{5GmM} \over {6R}}$
B.
${{2GmM} \over {3R}}$
C.
${{GmM} \over {2R}}$
D.
${{GmM} \over {3R}}$
2012
JEE Mains
MCQ
AIEEE 2012
The mass of a spaceship is $1000$ $kg.$ It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth ) are $10\,m/{s^2}$ and $6400$ $km$ respectively. The required energy for this work will be:
A.
$6.4 \times {10^{11}}\,$ Joules
B.
$6.4 \times {10^8}\,$ Joules
C.
$6.4 \times {10^9}\,$ Joules
D.
$6.4 \times {10^{10}}\,$ Joules
2011
JEE Mains
MCQ
AIEEE 2011
Two bodies of masses $m$ and $4$ $m$ are placed at a distance $r.$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:
A.
$ - {{4Gm} \over r}$
B.
$ - {{6Gm} \over r}$
C.
$ - {{9Gm} \over r}$
D.
zero
2009
JEE Mains
MCQ
AIEEE 2009
The height at which the acceleration due to gravity becomes ${g \over 9}$ (where $g=$ the acceleration due to gravity on the surface of the earth) in terms of $R,$ the radius of the earth, is:
A.
${R \over {\sqrt 2 }}$
B.
$R/2$
C.
$\sqrt 2 \,\,R$
D.
$2\,R$
2008
JEE Mains
MCQ
AIEEE 2008
This question contains Statement - $1$ and Statement - $2$. of the four choices given after the statements, choose the one that best describes the two statements.
Statement - $1$:
For a mass $M$ kept at the center of a cube of side $'a'$, the flux of gravitational field passing through its sides $4\,\pi \,GM.$
Statement - 2:
If the direction of a field due to a point source is radial and its dependence on the distance $'r'$ from the source is given as ${1 \over {{r^2}}},$ its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
Statement - $1$:
For a mass $M$ kept at the center of a cube of side $'a'$, the flux of gravitational field passing through its sides $4\,\pi \,GM.$
Statement - 2:
If the direction of a field due to a point source is radial and its dependence on the distance $'r'$ from the source is given as ${1 \over {{r^2}}},$ its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
A.
Statement - $1$ is false, Statement - $2$ is true
B.
Statement - $1$ is true, Statement - $2$ is true; Statement - $2$ is a correct explanation for Statement - $1$
C.
Statement - $1$ is true, Statement - $2$ is true; Statement - $2$ is not a correct explanation for Statement - $1$
D.
Statement - $1$ is true, Statement - $2$ is false
2008
JEE Mains
MCQ
AIEEE 2008
A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11\,\,km\,{s^{ - 1}},$ the escape velocity from the surface of the planet would be
A.
$1.1\,\,km\,{s^{ - 1}}$
B.
$100\,\,km\,{s^{ - 1}}$
C.
$110\,\,km\,{s^{ - 1}}$
D.
$0.11\,\,km\,{s^{ - 1}}$
2007
JEE Mains
MCQ
AIEEE 2007
If ${g_E}$ and ${g_M}$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio
${{electro\,\,ch\arg e\,\,on\,\,the\,\,moon} \over {electronic\,\,ch\arg e\,\,on\,\,the\,\,earth}}\,\,to\,be$
${{electro\,\,ch\arg e\,\,on\,\,the\,\,moon} \over {electronic\,\,ch\arg e\,\,on\,\,the\,\,earth}}\,\,to\,be$
A.
${g_M}/{g_E}$
B.
$1$
C.
$0$
D.
${g_E}/{g_M}$
2005
JEE Mains
MCQ
AIEEE 2005
The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?
A.
$d = {{3h} \over 2}$
B.
$d = {h \over 2}$
C.
$d = h$
D.
$d = 2\,h$
2005
JEE Mains
MCQ
AIEEE 2005
Average density of the earth
A.
is a complex function of $g$
B.
does not depend on $g$
C.
is inversely proportional to $g$
D.
is directly proportional to $g$
2005
JEE Mains
MCQ
AIEEE 2005
A particle of mass $10$ $g$ is kept on the surface of a uniform sphere of mass $100$ $kg$ and radius $10$ $cm.$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G$ $ = 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}$)
A.
$3.33 \times {10^{ - 10}}\,J$
B.
$13.34 \times {10^{ - 10}}\,J$
C.
$6.67 \times {10^{ - 10}}\,J$
D.
$6.67 \times {10^{ - 9}}\,J$
2004
JEE Mains
MCQ
AIEEE 2004
If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is
A.
${1 \over 4}mgR$
B.
$2mgR$
C.
${1 \over 2}mgR$
D.
$mgR$