-
question_answer1)
A body of mass m rises to height h = R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is [CPMT 1989; SCRA 1996; DPMT 2001]
A)
mgh done
clear
B)
\[\frac{4}{5}mgh\] done
clear
C)
\[\frac{5}{6}mgh\] done
clear
D)
\[\frac{6}{7}mgh\] done
clear
View Solution play_arrow
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question_answer2)
In a gravitational field, at a point where the gravitational potential is zero [CPMT 1990]
A)
The gravitational field is necessarily zero done
clear
B)
The gravitational field is not necessarily zero done
clear
C)
Nothing can be said definitely about the gravitational field done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer3)
The gravitational field due to a mass distribution is \[E=K/{{x}^{3}}\] in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is [MP PET 1994]
A)
\[K/x\] done
clear
B)
\[K/2x\] done
clear
C)
\[K/{{x}^{2}}\] done
clear
D)
\[K/2{{x}^{2}}\] done
clear
View Solution play_arrow
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question_answer4)
The mass of the earth is \[6.00\times {{10}^{24}}\,kg\] and that of the moon is \[7.40\times {{10}^{22}}\,kg\]. The constant of gravitation \[G=6.67\times {{10}^{-11}}\,N-{{m}^{2}}/k{{g}^{2}}\]. The potential energy of the system is \[-7.79\times {{10}^{28}}\,joules\]. The mean distance between the earth and moon is [MP PMT 1995]
A)
\[3.80\times {{10}^{8}}\,metres\] done
clear
B)
\[3.37\times {{10}^{6}}\,metres\] done
clear
C)
\[7.60\times {{10}^{4}}\,metres\] done
clear
D)
\[1.90\times {{10}^{2}}\,metres\] done
clear
View Solution play_arrow
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question_answer5)
The change in potential energy, when a body of mass m is raised to a height nR from the earth's surface is (R = Radius of earth) [MP PMT 1996]
A)
\[mgR\frac{n}{n-1}\] done
clear
B)
nmgR done
clear
C)
\[mgR\frac{{{n}^{2}}}{{{n}^{2}}+1}\] done
clear
D)
\[mgR\frac{n}{n+1}\] done
clear
View Solution play_arrow
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question_answer6)
The masses and radii of the earth and moon are \[{{M}_{1}},\,{{R}_{1}}\] and \[{{M}_{2}},\,{{R}_{2}}\] respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997]
A)
\[2\sqrt{\frac{G}{d}({{M}_{1}}+{{M}_{2}})}\] done
clear
B)
\[2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}\] done
clear
C)
\[2\sqrt{\frac{Gm}{d}({{M}_{1}}+{{M}_{2}})}\] done
clear
D)
\[2\sqrt{\frac{Gm({{M}_{1}}+{{M}_{2}})}{d({{R}_{1}}+{{R}_{2}})}}\] done
clear
View Solution play_arrow
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question_answer7)
If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be [RPET 1997]
A)
\[\sqrt{\frac{GM}{2R}}\] done
clear
B)
\[\frac{GM}{R}\] done
clear
C)
\[\sqrt{\frac{2GM}{R}}\] done
clear
D)
\[\frac{GM}{2R}\] done
clear
View Solution play_arrow
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question_answer8)
A rocket is launched with velocity 10 km/s. If radius of earth is R, then maximum height attained by it will be [RPET 1997]
A)
2R done
clear
B)
3R done
clear
C)
4R done
clear
D)
5R done
clear
View Solution play_arrow
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question_answer9)
There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of gravitational field will be zero [BHU 1997]
A)
\[\frac{1}{9}m\] done
clear
B)
\[\frac{1}{10}m\] done
clear
C)
\[\frac{1}{11}m\] done
clear
D)
\[\frac{10}{11}m\] done
clear
View Solution play_arrow
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question_answer10)
What is the intensity of gravitational field of the centre of a spherical shell [RPET 2000]
A)
\[Gm/{{r}^{2}}\] done
clear
B)
g done
clear
C)
Zero done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
The gravitational potential energy of a body of mass ?m? at the earth?s surface \[-mg{{R}_{e}}\]. Its gravitational potential energy at a height \[{{R}_{e}}\] from the earth?s surface will be (Here \[{{R}_{e}}\] is the radius of the earth) [AIIMS 2000; MP PET 2000; Pb. PMT 2004]
A)
\[-2\,mg{{R}_{e}}\] done
clear
B)
\[2\,mg{{R}_{e}}\] done
clear
C)
\[\frac{1}{2}mg{{R}_{e}}\] done
clear
D)
\[-\frac{1}{2}mg{{R}_{e}}\] done
clear
View Solution play_arrow
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question_answer12)
Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the Planet is [MP PMT 2002]
A)
? 5000 J done
clear
B)
? 1000 J done
clear
C)
? 2400 J done
clear
D)
5000 J done
clear
View Solution play_arrow
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question_answer13)
A body of mass m is placed on the earth?s surface. It is taken from the earth?s surface to a height \[h=3R\]. The change in gravitational potential energy of the body is [CBSE PMT 2002]
A)
\[\frac{2}{3}mgR\] done
clear
B)
\[\frac{3}{4}mgR\] done
clear
C)
\[\frac{mgR}{2}\] done
clear
D)
\[\frac{mgR}{4}\] done
clear
View Solution play_arrow
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question_answer14)
A body of mass m kg. starts falling from a point 2R above the Earth?s surface. Its kinetic energy when it has fallen to a point ?R? above the Earth?s surface [R-Radius of Earth, M-Mass of Earth, G-Gravitational Constant] [MP PMT 2002]
A)
\[\frac{1}{2}\frac{GMm}{R}\] done
clear
B)
\[\frac{1}{6}\frac{GMm}{R}\] done
clear
C)
\[\frac{2}{3}\frac{GMm}{R}\] done
clear
D)
\[\frac{1}{3}\frac{GMm}{R}\] done
clear
View Solution play_arrow
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question_answer15)
A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is [KCET (Engg./Med.) 2002]
A)
R/3 done
clear
B)
R/2 done
clear
C)
R/4 done
clear
D)
R/5 done
clear
View Solution play_arrow
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question_answer16)
Energy required to move a body of mass m from an orbit of radius 2R to 3R is [AIEEE 2002]
A)
\[GMm/12{{R}^{2}}\] done
clear
B)
\[GMm/3{{R}^{2}}\] done
clear
C)
\[GMm/8R\] done
clear
D)
\[GMm/6R\] done
clear
View Solution play_arrow
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question_answer17)
The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is [AIEEE 2002]
A)
mgR/2 done
clear
B)
2 mgR done
clear
C)
mgR done
clear
D)
mgR/4 done
clear
View Solution play_arrow
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question_answer18)
Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to [BHU 2003; CPMT 2004]
A)
\[\frac{1}{R}\] done
clear
B)
\[\frac{1}{\sqrt{R}}\] done
clear
C)
R done
clear
D)
\[\frac{1}{{{R}^{3/2}}}\] done
clear
View Solution play_arrow
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question_answer19)
In some region, the gravitational field is zero. The gravitational potential in this region [BVP 2003]
A)
Must be variable done
clear
B)
Must be constant done
clear
C)
Cannot be zero done
clear
D)
Must be zero done
clear
View Solution play_arrow
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question_answer20)
A particle falls towards earth from infinity. It?s velocity on reaching the earth would be [Orissa JEE 2003]
A)
Infinity done
clear
B)
\[\sqrt{2gR}\] done
clear
C)
\[2\sqrt{gR}\] done
clear
D)
Zero done
clear
View Solution play_arrow
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question_answer21)
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 : Mass of the planet Mass of the particle escaping Temperature of the planet Radius of the planet Select the correct answer from the codes given below: [SCRA 1994]
A)
I and II done
clear
B)
II and IV done
clear
C)
I and IV done
clear
D)
I, III and IV done
clear
View Solution play_arrow
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question_answer22)
\[{{v}_{e}}\] 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 [NCERT 1974; MP PMT 1994]
A)
\[{{v}_{e}}={{v}_{p}}\] done
clear
B)
\[{{v}_{e}}={{v}_{p}}/2\] done
clear
C)
\[{{v}_{e}}=2{{v}_{p}}\] done
clear
D)
\[{{v}_{e}}={{v}_{p}}/4\] done
clear
View Solution play_arrow
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question_answer23)
The escape velocity of a sphere of mass m from earth having mass M and radius R is given by [NCERT 1981, 84; CBSE PMT 1999]
A)
\[\sqrt{\frac{2GM}{R}}\] done
clear
B)
\[2\sqrt{\frac{GM}{R}}\] done
clear
C)
\[\sqrt{\frac{2GMm}{R}}\] done
clear
D)
\[\sqrt{\frac{GM}{R}}\] done
clear
View Solution play_arrow
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question_answer24)
The escape velocity for a rocket from earth is 11.2 km/sec. Its value on a planet where acceleration due to gravity is double that on the earth and diameter of the planet is twice that of earth will be in km/sec [NCERT 1983; CPMT 1990; MP PMT 2000; UPSEAT 1999]
A)
11.2 done
clear
B)
5.6 done
clear
C)
22.4 done
clear
D)
53.6 done
clear
View Solution play_arrow
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question_answer25)
The escape velocity from the earth is about 11 km/second. The escape velocity from a planet having twice the radius and the same mean density as the earth, is [NCERT 1980; MP PMT 1987; MP PET 2001, 2003; AIIMS 2001; UPSEAT 1999]
A)
22 km/sec done
clear
B)
11 km/sec done
clear
C)
5.5 km/sec done
clear
D)
15.5 km/sec done
clear
View Solution play_arrow
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question_answer26)
A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is [MNR 1986; MP PET 1995]
A)
Positive done
clear
B)
Negative done
clear
C)
Zero done
clear
D)
May be positive or negative depending upon its initial velocity done
clear
View Solution play_arrow
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question_answer27)
If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is [NCERT 1975; RPET 2003]
A)
gr done
clear
B)
\[\sqrt{2gr}\] done
clear
C)
\[g/r\] done
clear
D)
\[r/g\] done
clear
View Solution play_arrow
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question_answer28)
The escape velocity of a projectile from the earth is approximately [DPMT 1982, 84; RPMT 1997; BHU 1998]
A)
11.2 m/sec done
clear
B)
112 km/sec done
clear
C)
11.2 km/sec done
clear
D)
11200 km/sec done
clear
View Solution play_arrow
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question_answer29)
The escape velocity of a particle of mass m varies as [CPMT 1978; RPMT 1999; AIEEE 2002]
A)
\[{{m}^{2}}\] done
clear
B)
m done
clear
C)
\[{{m}^{0}}\] done
clear
D)
\[{{m}^{-1}}\] done
clear
View Solution play_arrow
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question_answer30)
For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of [MP PET 1994]
A)
2 done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[1/\sqrt{2}\] done
clear
D)
\[\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer31)
The escape velocity of an object from the earth depends upon the mass of the earth (M), its mean density \[(\rho )\], its radius (R) and the gravitational constant (G). Thus the formula for escape velocity is [MP PMT 1995]
A)
\[v=R\sqrt{\frac{8\pi }{3}G\rho }\] done
clear
B)
\[v=M\sqrt{\frac{8\pi }{3}GR}\] done
clear
C)
\[v=\sqrt{2GMR}\] done
clear
D)
\[v=\sqrt{\frac{2GM}{{{R}^{2}}}}\] done
clear
View Solution play_arrow
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question_answer32)
Escape velocity on a planet is \[{{v}_{e}}\]. If radius of the planet remains same and mass becomes 4 times, the escape velocity becomes [MP PMT 1996; DPMT 1999]
A)
\[4\,{{v}_{e}}\] done
clear
B)
\[2\,{{v}_{e}}\] done
clear
C)
\[{{v}_{e}}\] done
clear
D)
\[\frac{1}{2}{{v}_{e}}\] done
clear
View Solution play_arrow
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question_answer33)
The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5 times that of the moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be [MP PMT/PET 1998; JIPMER 2000]
A)
0.2 done
clear
B)
2.57 done
clear
C)
4.81 done
clear
D)
0.39 done
clear
View Solution play_arrow
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question_answer34)
The escape velocity from the surface of earth is \[{{V}_{e}}\]. The escape velocity from the surface of a planet whose mass and radius are 3 times those of the earth will be [MP PMT/PET 1998; JIPMER 2001, 02; Pb. PMT 2004]
A)
\[{{V}_{e}}\] done
clear
B)
\[3{{V}_{e}}\] done
clear
C)
\[9{{V}_{e}}\] done
clear
D)
\[27{{V}_{e}}\] done
clear
View Solution play_arrow
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question_answer35)
How much energy will be necessary for making a body of 500 kg escape from the earth \[[g=9.8\,m/{{s}^{2}}\], radius of earth \[=6.4\times {{10}^{6}}\,m]\] [MP PET 1999]
A)
About \[9.8\times {{10}^{6}}\,J\] done
clear
B)
About \[6.4\times {{10}^{8}}\,J\] done
clear
C)
About \[3.1\times {{10}^{10}}\,J\] done
clear
D)
About \[27.4\times {{10}^{12}}\,J\] done
clear
View Solution play_arrow
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question_answer36)
The escape velocity for the earth is 11.2 km/sec. The mass of another planet is 100 times that of the earth and its radius is 4 times that of the earth. The escape velocity for this planet will be [MP PMT 1999; Pb. PMT 2002]
A)
112.0 km/s done
clear
B)
5.6 km/s done
clear
C)
280.0 km/s done
clear
D)
56.0 km/s done
clear
View Solution play_arrow
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question_answer37)
The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is [CPMT 1999; MP PET 2003; Pb. PET 2002]
A)
\[\sqrt{3}\,{{V}_{e}}\] done
clear
B)
\[3\,{{V}_{e}}\] done
clear
C)
\[\sqrt{2}\,{{V}_{e}}\] done
clear
D)
\[2\,{{V}_{e}}\] done
clear
View Solution play_arrow
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question_answer38)
The escape velocity of an object on a planet whose g value is 9 times on earth and whose radius is 4 times that of earth in km/s is [EAMCET 1994]
A)
67.2 done
clear
B)
33.6 done
clear
C)
16.8 done
clear
D)
25.2 done
clear
View Solution play_arrow
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question_answer39)
The escape velocity on earth is 11.2 km/s. On another planet having twice radius and 8 times mass of the earth, the escape velocity will be [Bihar CMEET 1995]
A)
3.7 km/s done
clear
B)
11.2 km/s done
clear
C)
22.4 km/s done
clear
D)
43.2 km/s done
clear
View Solution play_arrow
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question_answer40)
The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become [CBSE PMT 1997]
A)
5.6 km/s done
clear
B)
11.2 km/s (remain unchanged) done
clear
C)
22.4 km/s done
clear
D)
44.8 km/s done
clear
View Solution play_arrow
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question_answer41)
Given mass of the moon is 1/81 of the mass of the earth and corresponding radius is 1/4 of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is [CPMT 1997; AIIMS 2000; Pb. PMT 2001]
A)
0.14 km/s done
clear
B)
0.5 km/s done
clear
C)
2.5 km/s done
clear
D)
5 km/s done
clear
View Solution play_arrow
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question_answer42)
The angular velocity of rotation of star (of mass M and radius R) at which the matter start to escape from its equator will be [MH CET 1999]
A)
\[\sqrt{\frac{2G{{M}^{2}}}{R}}\] done
clear
B)
\[\sqrt{\frac{2GM}{g}}\] done
clear
C)
\[\sqrt{\frac{2GM}{{{R}^{3}}}}\] done
clear
D)
\[\sqrt{\frac{2GR}{M}}\] done
clear
View Solution play_arrow
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question_answer43)
The least velocity required to throw a body away from the surface of a planet so that it may not return is (radius of the planet is \[6.4\times {{10}^{6}}m,\,\,g=9.8\,m/se{{c}^{2}})\] [AMU (Engg.) 1999]
A)
\[9.8\times {{10}^{-3}}m/sec\] done
clear
B)
\[12.8\times {{10}^{3}}m/sec\] done
clear
C)
\[9.8\times {{10}^{3}}m/sec\] done
clear
D)
\[11.2\times {{10}^{3}}m/sec\] done
clear
View Solution play_arrow
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question_answer44)
How many times is escape velocity \[({{V}_{e}})\], of orbital velocity \[({{V}_{0}})\] for a satellite revolving near earth [RPMT 2000]
A)
\[\sqrt{2}\] times done
clear
B)
2 times done
clear
C)
3 times done
clear
D)
4 times done
clear
View Solution play_arrow
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question_answer45)
Escape velocity on earth is 11.2 km/s. What would be the escape velocity on a planet whose mass is 1000 times and radius is 10 times that of earth [DCE 2001; DPMT 2004]
A)
112 km/s done
clear
B)
11.2 km/s done
clear
C)
1.12 km/s done
clear
D)
3.7 km/s done
clear
View Solution play_arrow
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question_answer46)
If the radius of a planet is R and its density is \[\rho \], the escape velocity from its surface will be [MP PMT 2001]
A)
\[{{v}_{e}}\propto \rho R\] done
clear
B)
\[{{v}_{e}}\propto \sqrt{\rho }R\] done
clear
C)
\[{{v}_{e}}\propto \frac{\sqrt{\rho }}{R}\] done
clear
D)
\[{{v}_{e}}\propto \frac{1}{\sqrt{\rho }R}\] done
clear
View Solution play_arrow
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question_answer47)
Escape velocity on the earth [BHU 2001]
A)
Is less than that on the moon done
clear
B)
Depends upon the mass of the body done
clear
C)
Depends upon the direction of projection done
clear
D)
Depends upon the height from which it is projected done
clear
View Solution play_arrow
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question_answer48)
If acceleration due to gravity on the surface of a planet is two times that on surface of earth and its radius is double that of earth. Then escape velocity from the surface of that planet in comparison to earth will be [RPET 2001]
A)
\[2{{v}_{e}}_{{}}\] done
clear
B)
\[3{{v}_{e}}_{{}}\] done
clear
C)
\[4{{v}_{e}}_{{}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer49)
The escape velocity of a rocket launched from the surface of the earth [UPSEAT 2001]
A)
Does not depend on the mass of the rocket done
clear
B)
Does not depend on the mass of the earth done
clear
C)
Depends on the mass of the planet towards which it is moving done
clear
D)
Depends on the mass of the rocket done
clear
View Solution play_arrow
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question_answer50)
The ratio of the radii of planets A and B is \[{{k}_{1}}\] and ratio of acceleration due to gravity on them is \[{{k}_{2}}\]. The ratio of escape velocities from them will be [BHU 2002]
A)
\[{{k}_{1}}{{k}_{2}}\] done
clear
B)
\[\sqrt{{{k}_{1}}{{k}_{2}}}\] done
clear
C)
\[\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\] done
clear
D)
\[\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}\] done
clear
View Solution play_arrow
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question_answer51)
A mass of \[6\times {{10}^{24}}kg\] is to be compressed in a sphere in such a way that the escape velocity from the sphere is \[3\times {{10}^{8}}m\,/s\]. Radius of the sphere should be \[(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})\] [UPSEAT 2002]
A)
9 km done
clear
B)
9 m done
clear
C)
9 cm done
clear
D)
9 mm done
clear
View Solution play_arrow
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question_answer52)
The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is \[({{v}_{e}}\] is the escape velocity of earth) [Kerala (Med.) 2002]
A)
\[\sqrt{2/3}\,{{v}_{e}}\] done
clear
B)
\[\sqrt{3/2}\,{{v}_{e}}\] done
clear
C)
\[\sqrt{2}/3\,{{v}_{e}}\] done
clear
D)
\[2/\sqrt{3}\,{{v}_{e}}\] done
clear
View Solution play_arrow
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question_answer53)
Escape velocity on the surface of earth is \[11.2\,km/s\]. Escape velocity from a planet whose mass is the same as that of earth and radius 1/4 that of earth is [CBSE PMT 2000; JIPMER 2002; BHU 2004]
A)
2.8 km/s done
clear
B)
15.6 km/s done
clear
C)
22.4 km/s done
clear
D)
44.8 km/s done
clear
View Solution play_arrow
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question_answer54)
The velocity with which a projectile must be fired so that it escapes earth?s gravitation does not depend on [AIIMS 2003]
A)
Mass of the earth done
clear
B)
Mass of the projectile done
clear
C)
Radius of the projectile?s orbit done
clear
D)
Gravitational constant done
clear
View Solution play_arrow
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question_answer55)
The radius of a planet is \[\frac{1}{4}\] of earth?s radius and its acceleration due to gravity is double that of earth?s acceleration due to gravity. How many times will the escape velocity at the planet?s surface be as compared to its value on earth?s surface [BCECE 2003; MH CET 2000]
A)
\[\frac{1}{\sqrt{2}}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[2\sqrt{2}\] done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer56)
The escape velocity for the earth is \[{{v}_{e}}\]. The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is [MP PET 2003]
A)
\[36\,{{v}_{e}}\] done
clear
B)
\[12\,{{v}_{e}}\] done
clear
C)
\[6\,{{v}_{e}}\] done
clear
D)
\[20\,{{v}_{e}}\] done
clear
View Solution play_arrow
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question_answer57)
The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45o with the vertical, the escape velocity will be [AIEEE 2003]
A)
\[\frac{11}{\sqrt{2}}km/s\] done
clear
B)
\[11\sqrt{2}\,km/s\] done
clear
C)
22 km/s done
clear
D)
11 km/s done
clear
View Solution play_arrow
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question_answer58)
If V, R and g denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is [MP PMT 2004]
A)
\[V=\sqrt{gR}\] done
clear
B)
\[V=\sqrt{\frac{4}{3}g{{R}^{3}}}\] done
clear
C)
\[V=R\sqrt{g}\] done
clear
D)
\[V=\sqrt{2gR}\] done
clear
View Solution play_arrow
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question_answer59)
The escape velocity for a body of mass 1 kg from the earth surface is \[11.2\,\,km{{s}^{-1}}.\] The escape velocity for a body of mass 100 kg would be [DCE 2003]
A)
\[11.2\times {{10}^{2}}\,km{{s}^{-1}}\] done
clear
B)
\[11.2\,\,km{{s}^{-1}}\] done
clear
C)
\[11.2\,\times {{10}^{-2}}\,km{{s}^{-1}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer60)
The acceleration due to gravity on a planet is same as that on earth and its radius is four times that of earth. What will be the value of escape velocity on that planet if it is \[{{v}_{e}}\] on earth [RPET 2002]
A)
\[{{v}_{e}}\] done
clear
B)
\[2{{v}_{e}}\] done
clear
C)
\[4{{v}_{e}}\] done
clear
D)
\[\frac{{{v}_{e}}}{2}\] done
clear
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question_answer61)
If the radius of a planet is four times that of earth and the value of g is same for both, the escape velocity on the planet will be [RPET 2002]
A)
\[11.2\,\,km/s\] done
clear
B)
\[5.6\,\,km/s\] done
clear
C)
\[22.4\,\,km/s\] done
clear
D)
None done
clear
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question_answer62)
If the radius and acceleration due to gravity both are doubled, escape velocity of earth will become [RPMT 2002]
A)
11.2 km/s done
clear
B)
22.4 km/s done
clear
C)
5.6 km/s done
clear
D)
44.8 km/s done
clear
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question_answer63)
A planet has twice the radius but the mean density is \[\frac{1}{4}th\] as compared to earth. What is the ratio of escape velocity from earth to that from the planet [MH CET 2004]
A)
3 : 1 done
clear
B)
1 : 2 done
clear
C)
1 : 1 done
clear
D)
2 : 1 done
clear
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question_answer64)
The escape velocity from earth is \[{{v}_{es}}.\] A body is projected with velocity \[2{{v}_{es}}\]with what constant velocity will it move in the inter planetary space [DCE 2002]
A)
\[{{v}_{es}}\] done
clear
B)
\[3{{v}_{es}}\] done
clear
C)
\[\sqrt{3}{{v}_{es}}\] done
clear
D)
\[\sqrt{5}{{v}_{es}}\] done
clear
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question_answer65)
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 \[G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}})\] [AIEEE 2005]
A)
\[6.67\times {{10}^{9}}J\] done
clear
B)
\[6.67\times {{10}^{10}}J\] done
clear
C)
\[13.34\times {{10}^{10}}J\] done
clear
D)
\[3.33\times {{10}^{10}}J\] done
clear
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question_answer66)
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is [CBSE PMT 2005]
A)
2 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{\sqrt{2}}\] done
clear
D)
\[\sqrt{2}\] done
clear
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question_answer67)
3 particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is [DCE 2005]
A)
Zero done
clear
B)
\[\frac{3GM}{{{L}^{2}}}\] done
clear
C)
\[\frac{9GM}{{{L}^{2}}}\] done
clear
D)
\[\frac{12}{\sqrt{3}}\,\frac{GM}{{{L}^{2}}}\] done
clear
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question_answer68)
The value of escape velocity on a certain planet is 2 km/s. Then the value of orbital speed for a satellite orbiting close to its surface is [DCE 2005]
A)
12 km/s done
clear
B)
1 km/s done
clear
C)
\[\sqrt{2}\]km/s done
clear
D)
\[2\sqrt{2}\,\,km/s\] done
clear
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question_answer69)
Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is [Kerala PET 2005]
A)
\[-\sqrt{32}\frac{GM}{L}\] done
clear
B)
\[-\sqrt{64}\frac{GM}{{{L}^{2}}}\] done
clear
C)
Zero done
clear
D)
\[\sqrt{32}\frac{GM}{L}\] done
clear
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question_answer70)
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 [BHU 2005]
A)
\[{{(Kg)}^{1/2}}\] done
clear
B)
\[{{(Kg)}^{-1/2}}\] done
clear
C)
\[{{(Kg)}^{2}}\] done
clear
D)
\[{{(Kg)}^{-2}}\] done
clear
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