Gravitation - 2 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A body of mass 100 kg falls on the earth from infinity.
What will be its energy on reaching the earth ? Radius of
the earth is 6400 km and g = 9.8 m/s
2
. Air friction is
negligible.
(a) 6.27 × 10
9 
J (b) 6.27 × 10
10 
J
(c) 6.27 × 10
10 
J (d) 6.27 × 10
7 
J
Q.2 An artificial satellite of the earth is to be established in the
equatorial plane of the earth and to an observer at the equator
it is required that the satellite will move eastward, completing
one round trip per day . The distance of the satellite from the
centre of the earth will be- (The mass of the earth is 6.00 ×
10
24
 kg and its angular velocity = 7.30 × 10
–5
 rad./sec.)
(a) 2.66 × 10
3 
m. (b) 2.66 × 10
5 
m.
(c) 2.66 × 10
6 
m. (d) 2.66 × 10
7 
m.
Q.3 Two satellites S
1
 and S
2
 revolve round a planet in the same
direction in circular orbits. Their periods of revolutions
are 1 hour and 8 hour respectively. The radius of S
1
 is 10
4
km. The velocity of S
2 
with respect to S
1
 will be-
(a) p × 10
4
 km/hr (b) p/3 × 10
4
 km/hr
(c)2p × 10
4
 km/hr (d) p/2 × 10
4
 km/hr
Q.4 In the above example the angular velocity of S
2
 as actually
observed by an astronaut in S
1
 is -
(a) p/3 rad/hr (b) p/3 rad/sec
(c) p/6 rad/hr (d)2p/7 rad/hr
Page 2


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A body of mass 100 kg falls on the earth from infinity.
What will be its energy on reaching the earth ? Radius of
the earth is 6400 km and g = 9.8 m/s
2
. Air friction is
negligible.
(a) 6.27 × 10
9 
J (b) 6.27 × 10
10 
J
(c) 6.27 × 10
10 
J (d) 6.27 × 10
7 
J
Q.2 An artificial satellite of the earth is to be established in the
equatorial plane of the earth and to an observer at the equator
it is required that the satellite will move eastward, completing
one round trip per day . The distance of the satellite from the
centre of the earth will be- (The mass of the earth is 6.00 ×
10
24
 kg and its angular velocity = 7.30 × 10
–5
 rad./sec.)
(a) 2.66 × 10
3 
m. (b) 2.66 × 10
5 
m.
(c) 2.66 × 10
6 
m. (d) 2.66 × 10
7 
m.
Q.3 Two satellites S
1
 and S
2
 revolve round a planet in the same
direction in circular orbits. Their periods of revolutions
are 1 hour and 8 hour respectively. The radius of S
1
 is 10
4
km. The velocity of S
2 
with respect to S
1
 will be-
(a) p × 10
4
 km/hr (b) p/3 × 10
4
 km/hr
(c)2p × 10
4
 km/hr (d) p/2 × 10
4
 km/hr
Q.4 In the above example the angular velocity of S
2
 as actually
observed by an astronaut in S
1
 is -
(a) p/3 rad/hr (b) p/3 rad/sec
(c) p/6 rad/hr (d)2p/7 rad/hr
2
DPP/ P 19
Q.5 The moon revolves round the earth 13 times in one year. If
the ratio of sun-earth distance to earth-moon distance is
392, then the ratio of masses of sun and earth will be -
(a) 365 (b) 356
(c) 3.56 × 10
5
 (d) 1
Q.6 Two planets of radii in the ratio 2 : 3 are made from the
materials of density in the ratio 3 : 2. Then the ratio of
acceleration due to gravity g
1
/g
2
 at the surface of two
planets will be
(a)1 (b) 2.25 (c)
4
9
(d) 0.12
Q.7 A satellite of mass m is revolving in a circular orbit of radius
r. The relation between the angular momentum J of satellite
and mass m of earth will be -
(a) J = 
2
G.Mmr
(b) J = 
GMm
(c) J = 
GMmr
(d) J = 
mr
M
Q.8 A spaceship is launched into a circular orbit close to earth's
surface. What additional velocity has now to be imparted
to the spaceship in the orbit to overcome the gravitational
pull? (Radius of earth = 6400 km, g = 9.8 m/sec
2
)
(a) 3.285 km/sec (b) 32.85 m/sec
(c) 11.32 km/sec (d) 7.32 m/sec
Q.9 The ratio of the radius of the Earth to that of the moon is
10. The ratio of g on earth to the moon is 6. The ratio of
the escape velocity from the earth’s surface to that from
the moon is approximately -
(a) 10 (b)8 (c)4 (d)2
Q.10 Acceleration due to gravity on a planet is 10 times the value
on the earth. Escape velocity for the planet and the earth
are V
p
 and V
e
 respectively. Assuming that the radii of the
planet and the earth are the same, then -
(a)V
P
 = 10 V
e
(b)V
P
 = 
10
 VV
e
(c)V
p 
= 
e
V
10
(d)V
P
 = 
e
V
10
Q.11 The Jupiter’s period of revolution round the Sun is 12 times
that of the Earth. Assuming the planetary orbits are circular,
how many times the distance between the Jupiter and Sun
exceeds that between the Earth and the sun.
(a) 5.242 (b) 4.242 (c) 3.242 (d) 2.242
Q.12The mean distance of mars from sun is 1.524 times the
distance of the earth from the sun. The period of revolution
of mars around sun will be-
(a) 2.88 earth year (b) 1.88 earth year
(c) 3.88 earth year (d) 4.88 earth year
Q.13 The semi-major axes of the orbits of mercury and mars are
respectively 0.387 and 1.524 in astronomical unit. If the
period of Mercury is 0.241 year, what is the period of Mars.
(a) 1.2 years (b) 3.2 years
(c) 3.9 years (d) 1.9 years
Q.14 If a graph is plotted between T
2
 and r
3
 for a planet then its
slope will be -
(a)
2
4
GM
p
(b)
2
GM
4p
(c)4p GM (d)0
Q.15 The mass and radius of earth and moon are M
1
, R
1
 and M
2
,
R
2
 respectively. Their centres are d distance apart. With
what velocity should a particle of mass m be projected from
the mid point of their centres so that it may escape out to
infinity -
(a)
12
G(M M)
d
+
(b)
12
2G(M M)
d
+
(c)
12
4G(M M)
d
+
(d)
12
GMM
d
Q.16 A satellite has to revolve round the earth in a circular orbit
of radius 8 × 10
3
 km. The velocity of projection of the
satellite in this orbit will be -
(a) 16 km/sec (b) 8 km/sec
(c) 3 km/sec (d) 7.08 km/sec
Q.17 If the satellite is stopped suddenly in its orbit which is at a
distnace = radius of earth from earth’s surface and allowed
to fall freely into the earth, the speed with which it hits the
surface of earth will be  -
(a) 7.919 m/sec (b) 7.919 km/sec
(c) 11.2 m/sec (d) 11.2  km/sec
Page 3


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A body of mass 100 kg falls on the earth from infinity.
What will be its energy on reaching the earth ? Radius of
the earth is 6400 km and g = 9.8 m/s
2
. Air friction is
negligible.
(a) 6.27 × 10
9 
J (b) 6.27 × 10
10 
J
(c) 6.27 × 10
10 
J (d) 6.27 × 10
7 
J
Q.2 An artificial satellite of the earth is to be established in the
equatorial plane of the earth and to an observer at the equator
it is required that the satellite will move eastward, completing
one round trip per day . The distance of the satellite from the
centre of the earth will be- (The mass of the earth is 6.00 ×
10
24
 kg and its angular velocity = 7.30 × 10
–5
 rad./sec.)
(a) 2.66 × 10
3 
m. (b) 2.66 × 10
5 
m.
(c) 2.66 × 10
6 
m. (d) 2.66 × 10
7 
m.
Q.3 Two satellites S
1
 and S
2
 revolve round a planet in the same
direction in circular orbits. Their periods of revolutions
are 1 hour and 8 hour respectively. The radius of S
1
 is 10
4
km. The velocity of S
2 
with respect to S
1
 will be-
(a) p × 10
4
 km/hr (b) p/3 × 10
4
 km/hr
(c)2p × 10
4
 km/hr (d) p/2 × 10
4
 km/hr
Q.4 In the above example the angular velocity of S
2
 as actually
observed by an astronaut in S
1
 is -
(a) p/3 rad/hr (b) p/3 rad/sec
(c) p/6 rad/hr (d)2p/7 rad/hr
2
DPP/ P 19
Q.5 The moon revolves round the earth 13 times in one year. If
the ratio of sun-earth distance to earth-moon distance is
392, then the ratio of masses of sun and earth will be -
(a) 365 (b) 356
(c) 3.56 × 10
5
 (d) 1
Q.6 Two planets of radii in the ratio 2 : 3 are made from the
materials of density in the ratio 3 : 2. Then the ratio of
acceleration due to gravity g
1
/g
2
 at the surface of two
planets will be
(a)1 (b) 2.25 (c)
4
9
(d) 0.12
Q.7 A satellite of mass m is revolving in a circular orbit of radius
r. The relation between the angular momentum J of satellite
and mass m of earth will be -
(a) J = 
2
G.Mmr
(b) J = 
GMm
(c) J = 
GMmr
(d) J = 
mr
M
Q.8 A spaceship is launched into a circular orbit close to earth's
surface. What additional velocity has now to be imparted
to the spaceship in the orbit to overcome the gravitational
pull? (Radius of earth = 6400 km, g = 9.8 m/sec
2
)
(a) 3.285 km/sec (b) 32.85 m/sec
(c) 11.32 km/sec (d) 7.32 m/sec
Q.9 The ratio of the radius of the Earth to that of the moon is
10. The ratio of g on earth to the moon is 6. The ratio of
the escape velocity from the earth’s surface to that from
the moon is approximately -
(a) 10 (b)8 (c)4 (d)2
Q.10 Acceleration due to gravity on a planet is 10 times the value
on the earth. Escape velocity for the planet and the earth
are V
p
 and V
e
 respectively. Assuming that the radii of the
planet and the earth are the same, then -
(a)V
P
 = 10 V
e
(b)V
P
 = 
10
 VV
e
(c)V
p 
= 
e
V
10
(d)V
P
 = 
e
V
10
Q.11 The Jupiter’s period of revolution round the Sun is 12 times
that of the Earth. Assuming the planetary orbits are circular,
how many times the distance between the Jupiter and Sun
exceeds that between the Earth and the sun.
(a) 5.242 (b) 4.242 (c) 3.242 (d) 2.242
Q.12The mean distance of mars from sun is 1.524 times the
distance of the earth from the sun. The period of revolution
of mars around sun will be-
(a) 2.88 earth year (b) 1.88 earth year
(c) 3.88 earth year (d) 4.88 earth year
Q.13 The semi-major axes of the orbits of mercury and mars are
respectively 0.387 and 1.524 in astronomical unit. If the
period of Mercury is 0.241 year, what is the period of Mars.
(a) 1.2 years (b) 3.2 years
(c) 3.9 years (d) 1.9 years
Q.14 If a graph is plotted between T
2
 and r
3
 for a planet then its
slope will be -
(a)
2
4
GM
p
(b)
2
GM
4p
(c)4p GM (d)0
Q.15 The mass and radius of earth and moon are M
1
, R
1
 and M
2
,
R
2
 respectively. Their centres are d distance apart. With
what velocity should a particle of mass m be projected from
the mid point of their centres so that it may escape out to
infinity -
(a)
12
G(M M)
d
+
(b)
12
2G(M M)
d
+
(c)
12
4G(M M)
d
+
(d)
12
GMM
d
Q.16 A satellite has to revolve round the earth in a circular orbit
of radius 8 × 10
3
 km. The velocity of projection of the
satellite in this orbit will be -
(a) 16 km/sec (b) 8 km/sec
(c) 3 km/sec (d) 7.08 km/sec
Q.17 If the satellite is stopped suddenly in its orbit which is at a
distnace = radius of earth from earth’s surface and allowed
to fall freely into the earth, the speed with which it hits the
surface of earth will be  -
(a) 7.919 m/sec (b) 7.919 km/sec
(c) 11.2 m/sec (d) 11.2  km/sec
DPP/ P 19
3
Q.18 A projectile is fired vertically upward from the surface of
earth with a velocity K v
e
 m/s where v
e
 m/s is the escape
velocity and K < 1. Neglecting air resistance, the maximum
height to which it will rise measured from the centre of
the earth is - (where R = radius of earth)
(a)
2
R
1K -
(b)
2
R
K
(c)
2
1K
R
-
(d)
2
K
R
Q.19A satellite is revolving in an orbit close to the earth’s
surface. Taking the radius of the earth as 6.4 × 10
6
 metre,
the value of the orbital speed and the period of revolution
of the satellite will respectively be (g = 9.8 meter/sec
2
)
(a) 7.2 km/sec., 84.6 minutes
(b) 2.7 km/sec., 8.6 minutes
(c) .72 km/sec., 84.6 minutes
(d) 7.2 km/sec., 8.6 minutes
Q.20 If the period of revolution of an artificial satellite just above
the earth be T second and the density of earth be r, kg/m
3
then
(G = 6.67 × 10
–11
 m
3
/kg. second
2
)
(a)
r
T
2
 is a universal constant
(b)
r
T
2
 varies with time
(c)
r
T
2
 = 
3
G
p
(d) Both (a) and (c)
Q.21 Two satellites P and Q of same mass are revolving near the
earth surface in the equitorial plane. The satellite P moves
in the direction of rotation of earth whereas Q moves in
the opposite direction. The ratio of their kinetic energies
with respect to a frame attached to earth will be -
(a)  
2
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(b)  
2
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(c)
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(d)
7437
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DIRECTIONS (Q.22-Q.24) : In the following questions, more than
one of the answers  given are correct. Select the correct answers
and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 Gas escapes from the surface of a planet because it acquires
an escape velocity. The escape velocity will depend on
which of the following factors:
(1) Mass of the planet
(2) Radius of the planet
(3) Mass of the particle escaping
(4) Temperature of the planet
Q.23 v
e
 and v
p
 denotes the escape velocity from the earth and
another planet having twice the radius and the same mean
density as the earth. Then which of the following is (are)
wrong ?
(1) v
e
 = v
p
(2) v
e
 = 2v
p
(3) v
e
 = v
p
/4 (4) v
e
 = v
p
 / 2
Q.24 Select the wrong statements from the following
(1) The orbital velocity of a satellite increases with the
radius of the orbit
(2) Escape velocity of a particle from the surface of the
earth depends on the speed with which it is fired
(3) The time period of a satellite does not depend on the
radius of the orbit
(4) The orbital velocity is inversely proportional to the
square root of the radius of the orbit
DIRECTIONS (Q.25-Q.27) : Read the passage given below and
answer the questions that follows :
It can be assumed that orbits of earth and mars are nearly circular
around the sun. It is proposed to launch an artificial planet around
the sun such that its apogee is at the orbit of mars while its perigee
is at the orbit of earth. Let T
e
 and T
m
 be periods of revolution of
earth and mars. Further the variables are assigned the meanings as
follows.
M
e
 ® Mass of earth
M
m
 ® Mass of mars.
L
e
 ® Angular momentum of earth around the sun.
L
m
 ® Angular momentum of mars around the sun.
R
e
 ® Semi major axis of earth’s orbit.
R
m
 ® Semi major axis of mars orbit.
M ® Mass of the artificial planet.
E
e
 ® Total energy of earth.
E
m
 ® Total energy of mars.
Page 4


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A body of mass 100 kg falls on the earth from infinity.
What will be its energy on reaching the earth ? Radius of
the earth is 6400 km and g = 9.8 m/s
2
. Air friction is
negligible.
(a) 6.27 × 10
9 
J (b) 6.27 × 10
10 
J
(c) 6.27 × 10
10 
J (d) 6.27 × 10
7 
J
Q.2 An artificial satellite of the earth is to be established in the
equatorial plane of the earth and to an observer at the equator
it is required that the satellite will move eastward, completing
one round trip per day . The distance of the satellite from the
centre of the earth will be- (The mass of the earth is 6.00 ×
10
24
 kg and its angular velocity = 7.30 × 10
–5
 rad./sec.)
(a) 2.66 × 10
3 
m. (b) 2.66 × 10
5 
m.
(c) 2.66 × 10
6 
m. (d) 2.66 × 10
7 
m.
Q.3 Two satellites S
1
 and S
2
 revolve round a planet in the same
direction in circular orbits. Their periods of revolutions
are 1 hour and 8 hour respectively. The radius of S
1
 is 10
4
km. The velocity of S
2 
with respect to S
1
 will be-
(a) p × 10
4
 km/hr (b) p/3 × 10
4
 km/hr
(c)2p × 10
4
 km/hr (d) p/2 × 10
4
 km/hr
Q.4 In the above example the angular velocity of S
2
 as actually
observed by an astronaut in S
1
 is -
(a) p/3 rad/hr (b) p/3 rad/sec
(c) p/6 rad/hr (d)2p/7 rad/hr
2
DPP/ P 19
Q.5 The moon revolves round the earth 13 times in one year. If
the ratio of sun-earth distance to earth-moon distance is
392, then the ratio of masses of sun and earth will be -
(a) 365 (b) 356
(c) 3.56 × 10
5
 (d) 1
Q.6 Two planets of radii in the ratio 2 : 3 are made from the
materials of density in the ratio 3 : 2. Then the ratio of
acceleration due to gravity g
1
/g
2
 at the surface of two
planets will be
(a)1 (b) 2.25 (c)
4
9
(d) 0.12
Q.7 A satellite of mass m is revolving in a circular orbit of radius
r. The relation between the angular momentum J of satellite
and mass m of earth will be -
(a) J = 
2
G.Mmr
(b) J = 
GMm
(c) J = 
GMmr
(d) J = 
mr
M
Q.8 A spaceship is launched into a circular orbit close to earth's
surface. What additional velocity has now to be imparted
to the spaceship in the orbit to overcome the gravitational
pull? (Radius of earth = 6400 km, g = 9.8 m/sec
2
)
(a) 3.285 km/sec (b) 32.85 m/sec
(c) 11.32 km/sec (d) 7.32 m/sec
Q.9 The ratio of the radius of the Earth to that of the moon is
10. The ratio of g on earth to the moon is 6. The ratio of
the escape velocity from the earth’s surface to that from
the moon is approximately -
(a) 10 (b)8 (c)4 (d)2
Q.10 Acceleration due to gravity on a planet is 10 times the value
on the earth. Escape velocity for the planet and the earth
are V
p
 and V
e
 respectively. Assuming that the radii of the
planet and the earth are the same, then -
(a)V
P
 = 10 V
e
(b)V
P
 = 
10
 VV
e
(c)V
p 
= 
e
V
10
(d)V
P
 = 
e
V
10
Q.11 The Jupiter’s period of revolution round the Sun is 12 times
that of the Earth. Assuming the planetary orbits are circular,
how many times the distance between the Jupiter and Sun
exceeds that between the Earth and the sun.
(a) 5.242 (b) 4.242 (c) 3.242 (d) 2.242
Q.12The mean distance of mars from sun is 1.524 times the
distance of the earth from the sun. The period of revolution
of mars around sun will be-
(a) 2.88 earth year (b) 1.88 earth year
(c) 3.88 earth year (d) 4.88 earth year
Q.13 The semi-major axes of the orbits of mercury and mars are
respectively 0.387 and 1.524 in astronomical unit. If the
period of Mercury is 0.241 year, what is the period of Mars.
(a) 1.2 years (b) 3.2 years
(c) 3.9 years (d) 1.9 years
Q.14 If a graph is plotted between T
2
 and r
3
 for a planet then its
slope will be -
(a)
2
4
GM
p
(b)
2
GM
4p
(c)4p GM (d)0
Q.15 The mass and radius of earth and moon are M
1
, R
1
 and M
2
,
R
2
 respectively. Their centres are d distance apart. With
what velocity should a particle of mass m be projected from
the mid point of their centres so that it may escape out to
infinity -
(a)
12
G(M M)
d
+
(b)
12
2G(M M)
d
+
(c)
12
4G(M M)
d
+
(d)
12
GMM
d
Q.16 A satellite has to revolve round the earth in a circular orbit
of radius 8 × 10
3
 km. The velocity of projection of the
satellite in this orbit will be -
(a) 16 km/sec (b) 8 km/sec
(c) 3 km/sec (d) 7.08 km/sec
Q.17 If the satellite is stopped suddenly in its orbit which is at a
distnace = radius of earth from earth’s surface and allowed
to fall freely into the earth, the speed with which it hits the
surface of earth will be  -
(a) 7.919 m/sec (b) 7.919 km/sec
(c) 11.2 m/sec (d) 11.2  km/sec
DPP/ P 19
3
Q.18 A projectile is fired vertically upward from the surface of
earth with a velocity K v
e
 m/s where v
e
 m/s is the escape
velocity and K < 1. Neglecting air resistance, the maximum
height to which it will rise measured from the centre of
the earth is - (where R = radius of earth)
(a)
2
R
1K -
(b)
2
R
K
(c)
2
1K
R
-
(d)
2
K
R
Q.19A satellite is revolving in an orbit close to the earth’s
surface. Taking the radius of the earth as 6.4 × 10
6
 metre,
the value of the orbital speed and the period of revolution
of the satellite will respectively be (g = 9.8 meter/sec
2
)
(a) 7.2 km/sec., 84.6 minutes
(b) 2.7 km/sec., 8.6 minutes
(c) .72 km/sec., 84.6 minutes
(d) 7.2 km/sec., 8.6 minutes
Q.20 If the period of revolution of an artificial satellite just above
the earth be T second and the density of earth be r, kg/m
3
then
(G = 6.67 × 10
–11
 m
3
/kg. second
2
)
(a)
r
T
2
 is a universal constant
(b)
r
T
2
 varies with time
(c)
r
T
2
 = 
3
G
p
(d) Both (a) and (c)
Q.21 Two satellites P and Q of same mass are revolving near the
earth surface in the equitorial plane. The satellite P moves
in the direction of rotation of earth whereas Q moves in
the opposite direction. The ratio of their kinetic energies
with respect to a frame attached to earth will be -
(a)  
2
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(b)  
2
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(c)
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ç÷
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(d)
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8363
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ç÷
èø
DIRECTIONS (Q.22-Q.24) : In the following questions, more than
one of the answers  given are correct. Select the correct answers
and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 Gas escapes from the surface of a planet because it acquires
an escape velocity. The escape velocity will depend on
which of the following factors:
(1) Mass of the planet
(2) Radius of the planet
(3) Mass of the particle escaping
(4) Temperature of the planet
Q.23 v
e
 and v
p
 denotes the escape velocity from the earth and
another planet having twice the radius and the same mean
density as the earth. Then which of the following is (are)
wrong ?
(1) v
e
 = v
p
(2) v
e
 = 2v
p
(3) v
e
 = v
p
/4 (4) v
e
 = v
p
 / 2
Q.24 Select the wrong statements from the following
(1) The orbital velocity of a satellite increases with the
radius of the orbit
(2) Escape velocity of a particle from the surface of the
earth depends on the speed with which it is fired
(3) The time period of a satellite does not depend on the
radius of the orbit
(4) The orbital velocity is inversely proportional to the
square root of the radius of the orbit
DIRECTIONS (Q.25-Q.27) : Read the passage given below and
answer the questions that follows :
It can be assumed that orbits of earth and mars are nearly circular
around the sun. It is proposed to launch an artificial planet around
the sun such that its apogee is at the orbit of mars while its perigee
is at the orbit of earth. Let T
e
 and T
m
 be periods of revolution of
earth and mars. Further the variables are assigned the meanings as
follows.
M
e
 ® Mass of earth
M
m
 ® Mass of mars.
L
e
 ® Angular momentum of earth around the sun.
L
m
 ® Angular momentum of mars around the sun.
R
e
 ® Semi major axis of earth’s orbit.
R
m
 ® Semi major axis of mars orbit.
M ® Mass of the artificial planet.
E
e
 ® Total energy of earth.
E
m
 ® Total energy of mars.
4
DPP/ P 19
Q.25 Time period of revolution of the artificial planet about sun
will be (neglect gravitational effects of earth and mars)
(a)
2
em
TT +
(b)
em
TT
(c)
2
em
em
TT
TT +
(d)
3/2
2/3 2/3
2
em
TT
éù
+
êú
êú
ëû
Q.26 The total energy of the artificial planet’s orbit will be
(a)
2
ee
e em
RE M
M RR
æö
ç÷
+ èø
(b)
2
ee
m em
RE M
M RR
æö
ç÷
+ èø
(c)
2
e em
mm
EM RR
MR
æö +
ç÷
èø
(d)
22
2
e em
e
em
EM RR
M
RR
æö
+
ç÷
ç÷
+
èø
Q.27 Areal velocity of the artificial planet around the sun will
be
(a) less than that of earth
(b) more than that of mars
(c) more than that of earth
(d) same as that of the earth
DIRECTIONS (Q. 28-Q.30) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select
the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
Q.28Statement-1 :The speed of revolution of an artificial
satellite revolving very near the earth is 8kms
–1
.
Statement-2 : Orbital velocity of a satellite, become
independent of height of near satellite.
Q.29 Statement-1 :If an earth satellite moves to a lower orbit,
there is some dissipation of energy but the speed of
gravitational satellite increases.
Statement-2 :The speed of satellite is a constant quantity.
Q.30 Statement-1 :Gravitational potential of earth at every place
on it is negative.
Statement-2 :Every body on earth is bound by the attraction
of earth.