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JEE Questions for Physics Gravitation Quiz 2 - MCQExams.com
JEE
Physics
Gravitation
Quiz 2
If g is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth is
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0%
0%
2)
0%
mgR
0%
2mgR
The gravitational potential energy of a body of mass m at a distance r from the centre of the earth is U . What is the weight of the body at this distance?
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U
0%
Ur
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0%
The potential energy of 4-particles each of mass 1kg placed at the four vertices of a square of side length 1m is
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+ 4.0 G
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– 7.5 G
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– 5.4 G
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+ 6.3 G
If an object of mass m is taken from the surface of earth (radius R) to a height 2R, then the work done is
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2mgR
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mgR
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0%
0%
The escape velocity from the earth is 11 kms
-1
. The escape velocity from a planet having twice the radius and same mean density as that of earth is
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5.5 kms -1
0%
11 kms -1
0%
22 kms -1
0%
None of these
A body is orbiting very close to the earth\'s surface with kinetic energy KE. The energy required to completely escape from it is
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KE
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2 KE
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0%
The escape velocity from the earth is 11.2 kms
-1
. The escape velocity from a planet having twice the radius and the same mean density is (in kms
-1
)
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11.2
0%
5.6
0%
15
0%
22.4
The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is
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0%
√3v
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√2v
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v
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√5v
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√12v
Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)
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2)
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0%
The energy of the mass m remains constant
The total energy of an artificial satellite of mass m revolving in a circular orbit around the earth with a speed v is
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0%
2)
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0%
0%
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and R in a circular orbit an altitude of 2R?
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0%
2)
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0%
A satellite is moving with a constant speed v in a circular orbit about 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 its ejection, the kinetic energy of the object is
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0%
2)
0%
0%
A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R. The ratio of their respective periods is
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4 : 1
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1 : 8
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8 : 1
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1 : 4
0%
1 : 2
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0%
0%
24 nh
0%
0%
24 n2h
If ρ is the density of the planet, the time period of near by satellite is given by
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0%
2)
0%
0%
Rockets are launched in eastward direction to take advantage of
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the clear sky on Eastern side
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the thinner atmosphere on this side
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earth's rotation
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earth's tilt
The period of a planet around sun is 27 times that of the earth. The ratio of radius of planet\'s orbit to the radius of the earth\'s orbit is
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4
0%
9
0%
64
0%
27
A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is
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2E
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2)
0%
E/2
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0%
E
A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3R around the same planet will have a period (in hour)
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0%
16
0%
4
0%
4√27
0%
4√8
A body is orbiting around the earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is
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4 days
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16 days
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2√2 days
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64 days
The time period of an earth satellite in circular orbit is independent of
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the mass of the satellite
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radius of its orbit
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both the mass and radius of the orbit
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Neither the mass of the satellite nor the radius of its orbit
A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased
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0%
100 %
0%
41.4 %
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50 %
0%
59.6 %
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T2 is proportional to R3
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T2 is proportional to R7/2
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T2 is proportional to R3/2
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T2 is proportional to R3/73
A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R / 2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R / 4 from the centre of sphere. The gravitational pull between the sphere and the point mass m is
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0%
2)
0%
0%
Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L . They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is
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0%
2)
0%
0%
0%
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0%
2R
0%
2)
0%
0%
If the density of the earth is doubled keeping radius constant, find the new acceleration due to gravity ? (take, g = 9.8 m/s
2
)
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9.8 m/s2
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19.6 m/s2
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4.9 m/s2
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39.2 m/s2
The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B?
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6 m
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2/3 m
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2/9 m
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18 m
Acceleration due to gravity is g on the surface of the earth. Then, the value of the acceleration due to gravity at a height of 32 km above earth's surface is (assume radius of earth to be 6400 km)
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0.99 g
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0.8 g
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1.01 g
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0.9 g
The radius of the earth is R. The height of a point vertically above the earth\'s surface at which acceleration due to gravity becomes 1% of its value at the surface is
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8 R
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9 R
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10 R
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20 R
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?
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0%
2)
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d = 2h
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d = h
Weight of a body of mass m decreases by 1% when it is raised to height h above the earth\'s surface. If the body is taken to a depth h in a mine, change in its weight is
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0%
0.5% decrease
0%
2% decrease
0%
0.5% increase
0%
1% increase
Assuming the earth to be a sphere of radius R, if g
30°
. is value of acceleration due to gravity at latitude of 30° and g at the equator, the value of g – g
30°
is
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0%
2)
0%
0%
Two spherical planets P and Q have the same uniform density ρ, passes M
P
and M
Q
and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is (M
P
+ M
Q
). The escape velocities from the planets P, Q and R, are v
P
, v
Q
and v
R
, respectively. Then,
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vQ > vR > vP
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vR > vQ > vP
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vR / vP = 3
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vP / vQ = 1/2
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5
0%
7
0%
3
0%
11
A body is released from a point distance r from the centre of earth. If R is the radius of the earth and r > R , then the velocity of the body at the time of striking the earth will be
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0%
2)
0%
0%
A mass of 6 × 10
24
kg is to be compressed in a sphere in such a way that the escape velocity from the sphere is 3 × 10
8
m/s. What should be the radius of the sphere? (take, G = 6.67 × 10
-11
Nm
2
/kg
2
)
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9 km
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9 m
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9 cm
0%
9 mm
A body of mass 500 g is thrown upward with a velocity 20 ms
-1
and reaches back to the surface of a planet after 20s. Then, the weight of the body on that planet is
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2 N
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4 N
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5 N
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1 N
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 kms
-1
, the escape velocity from the surface of the planet would be
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1.1 kms -1
0%
11 kms -1
0%
110 kms -1
0%
0.11 kms -1
If g is the acceleration due to gravity on earth's surface, the gain of 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
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0%
2 mgR
0%
mgR
0%
0%
Infinite number of masses each 1 kg are placed along the X–axis at x = ± lm, ± 2m, ± 4m, ± 8m, ± 16 m.... The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x =is
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G/2
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G
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2G
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4G
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8G
There are two planets. The ratio of radius of the two planets is K but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity ?
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( kg ) 1/2
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( kg ) -1/2
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( kg ) 2
0%
( kg ) -2
A body is projected upwards with a velocity of 4 × 11.2 kms
-1
from the surface of earth. What will be the velocity of the body when it escapes from the gravitational pull of the earth?
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11.2 kms -1
0%
2 × 11.2 kms -1
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3 × 11.2 kms -1
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√15 × 11.2 kms -1
The escape velocity of a projectile on the earth's surface is 11.2 kms
-1
. A body is projected out with thrice this speed. The speed of the body far away from the earth will be
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0%
22.4 kms -1
0%
31.7 kms -1
0%
33.6 kms -1
0%
None of these
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. (take, G = 6.67 × 10
-11
Nm
2
-kg
-2
)
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13.34 × 10-10 J
0%
3.33 × 10-10 J
0%
6.67 × 10-9 J
0%
6.67 × 10-10 J
What is a period of revolution of the earth satellite? Ignore the height of satellite above the surface of the earth. Given, the value of gravitational acceleration g = 10 ms
-2
, radius of the earth R
e
= 6400 km. (take, π = 3.
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90 min
0%
85 min
0%
156 min
0%
83.73 min
A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7 R , the minimum energy required to be spent by the launching vehicle on the satellite is [Gravitational constant = G]
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0%
A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distances of the planet from the sun are r
1
and r
2
respectively. The time period of the planet is proportional to
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( r1 + r2 )
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( r1 + r2 ) 1/2
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( r1 - r2 ) 3/2
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( r1 + r2 ) 3/2
A satellite is revolving around the planet. The gravitational force between them varies with R
-5/2
, where R is the radius of the satellite. The square of the time period T will be directly proportional to
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R3
0%
R7/2
0%
R3/2
0%
R5/7
A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth, R being the radius of the earth. What will be the time period of another satellite at a height 2.5R from the surface of the earth?
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0%
2)
0%
0%
12 h
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