JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank

done Kepler's Laws of Planetary Motion Total Questions - 51

• question_answer1)
  The distance of neptune and saturn from sun are nearly \[{{10}^{13}}\] and \[{{10}^{12}}\] meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio          [NCERT 1975; CBSE PMT 1994; MP PET 2001]
  A)
              \[\sqrt{10}\]     done clear
  B)
              100 done clear
  C)
              \[10\sqrt{10}\] done clear
  D)
                \[1/\sqrt{10}\] done clear
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• question_answer2)
  The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If \[{{t}_{1}}\] and \[{{t}_{2}}\] represent the time for the planet to move from a to b and d to c respectively, then       [CPMT 1986, 88]
  A)
              \[{{t}_{1}}<{{t}_{2}}\]      done clear
  B)
              \[{{t}_{1}}>{{t}_{2}}\] done clear
  C)
              \[{{t}_{1}}={{t}_{2}}\] done clear
  D)
              \[{{t}_{1}}\le {{t}_{2}}\] done clear
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• question_answer3)
  The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R is             [CPMT 1982; MP PET/PMT 1998; AIIMS 2000; CBSE PMT 2002]
  A)
  4T done clear
  B)
                T/4 done clear
  C)
              8T        done clear
  D)
               T/8 done clear
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• question_answer4)
  Orbit of a planet around a star is                      [CPMT 1982]
  A)
  A circle done clear
  B)
                An ellipse done clear
  C)
              A parabola done clear
  D)
                A straight line done clear
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• question_answer5)
  If a body describes a circular motion under inverse square field, the time taken to complete one revolution T is related to the radius of the circular orbit as [NCERT 1975; RPMT 2000]
  A)
              \[T\propto r\]    done clear
  B)
              \[T\propto {{r}^{2}}\] done clear
  C)
              \[{{T}^{2}}\propto {{r}^{3}}\] done clear
  D)
                \[T\propto {{r}^{4}}\] done clear
  View Solution play_arrow

• question_answer6)
  If the earth is at one-fourth of its present distance from the sun, the duration of the year will be        [EAMCET 1987]
  A)
  Half the present year done clear
  B)
              One-eighth the present year done clear
  C)
              One-fourth the present year done clear
  D)
              One-sixth the present year done clear
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• question_answer7)
  The earth revolves about the sun in an elliptical orbit with mean radius \[9.3\times {{10}^{7}}\,m\] in a period of 1 year. Assuming that there are no outside influences
  A)
  The earth's kinetic energy remains constant done clear
  B)
              The earth's angular momentum remains constant done clear
  C)
              The earth's potential energy remains constant done clear
  D)
              All are correct done clear
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• question_answer8)
  Venus looks brighter than other planets because [MNR 1985]
  A)
  It is heavier than other planets done clear
  B)
              It has higher density than other planets done clear
  C)
              It is closer to the earth than other planets done clear
  D)
              It has no atmosphere done clear
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• question_answer9)
  A planet moves around the sun. At a given point P, it is closest from the sun at a distance \[{{d}_{1}}\] and has a speed \[{{v}_{1}}\]. At another point Q,  when  it is farthest from the sun at a distance \[{{d}_{2}}\], its speed will be [MP PMT 1987; DCE 2002]
  A)
              \[\frac{d_{1}^{2}{{v}_{1}}}{d_{2}^{2}}\]       done clear
  B)
              \[\frac{{{d}_{2}}{{v}_{1}}}{{{d}_{1}}}\] done clear
  C)
              \[\frac{{{d}_{1}}{{v}_{1}}}{{{d}_{2}}}\]           done clear
  D)
              \[\frac{d_{2}^{2}{{v}_{1}}}{d_{1}^{2}}\] done clear
  View Solution play_arrow

• question_answer10)
  The orbital speed of Jupiter is [MNR 1986; UPSEAT 2000]
  A)
  Greater than the orbital speed of earth done clear
  B)
              Less than the orbital speed of earth done clear
  C)
              Equal to the orbital speed of earth done clear
  D)
              Zero done clear
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• question_answer11)
  Two planets move around the sun. The periodic times and the mean radii of the orbits are \[{{T}_{1}},\,{{T}_{2}}\] and \[{{r}_{1}},\,{{r}_{2}}\] respectively. The ratio \[{{T}_{1}}/{{T}_{2}}\] is equal to                                    [CPMT 1978]
  A)
              \[{{({{r}_{1}}/{{r}_{2}})}^{1/2}}\] done clear
  B)
                \[{{r}_{1}}/{{r}_{2}}\] done clear
  C)
              \[{{({{r}_{1}}/{{r}_{2}})}^{2}}\] done clear
  D)
                \[{{({{r}_{1}}/{{r}_{2}})}^{3/2}}\] done clear
  View Solution play_arrow

• question_answer12)
  Kepler's second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation of         [CPMT 1990; AIIMS 2002]
  A)
  Energy done clear
  B)
                Angular momentum done clear
  C)
              Linear momentum       done clear
  D)
              None of these done clear
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• question_answer13)
  The largest and the shortest distance of the earth from the sun are \[{{r}_{1}}\] and \[{{r}_{2}}\], its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun                                                [CBSE PMT 1991]
  A)
              \[\frac{{{r}_{1}}+{{r}_{2}}}{4}\] done clear
  B)
              \[\frac{{{r}_{1}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\] done clear
  C)
              \[\frac{2{{r}_{1}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}\]  done clear
  D)
              \[\frac{{{r}_{1}}+{{r}_{2}}}{3}\] done clear
  View Solution play_arrow

• question_answer14)
  The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be      [MP PMT 1994]
  A)
  83 minutes done clear
  B)
                \[83\times \sqrt{8}\] minutes done clear
  C)
              664 minutes done clear
  D)
                249 minutes done clear
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• question_answer15)
  A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is \[{{R}_{0}}\] and mass of the earth M, the angular momentum about the centre of the earth is       [MP PMT 1996; RPMT 2000]
  A)
              \[m\sqrt{GM{{R}_{0}}}\] done clear
  B)
                \[M\sqrt{Gm{{R}_{0}}}\] done clear
  C)
              \[m\sqrt{\frac{GM}{{{R}_{0}}}}\]  done clear
  D)
              \[M\sqrt{\frac{GM}{{{R}_{0}}}}\] done clear
  View Solution play_arrow

• question_answer16)
  According to Kepler, the period of revolution of a planet (T) and its mean distance from the sun (r) are related by the equation [EAMCET (Med.) 1995; MH CET 2000; Pb. PET 2001]
  A)
              \[{{T}^{3}}{{r}^{3}}=\] constant           done clear
  B)
              \[{{T}^{2}}{{r}^{-3}}=\]constant done clear
  C)
                \[T{{r}^{3}}=\] constant     done clear
  D)
              \[{{T}^{2}}r=\] constant done clear
  View Solution play_arrow

• question_answer17)
  A planet revolves around sun whose mean distance is 1.588 times the mean distance between earth and sun. The revolution time of planet will be                       [RPET 1997]
  A)
  1.25 years done clear
  B)
                1.59 years done clear
  C)
              0.89 years done clear
  D)
                2 years done clear
  View Solution play_arrow

• question_answer18)
  A satellite A of mass m is at a distance of r from the centre of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's centre. Their time periods are in the ratio of                 [CBSE PMT 1993]
  A)
  1 : 2     done clear
  B)
              1 : 16 done clear
  C)
              1 : 32   done clear
  D)
              \[1:2\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer19)
  The earth E moves in an elliptical orbit with the sun S at one of the foci as shown in figure. Its speed of motion will be maximum at the point                     [BHU 1994; CPMT 1997]    
  A)
  C done clear
  B)
              A done clear
  C)
              B done clear
  D)
              D done clear
  View Solution play_arrow

• question_answer20)
  The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun [CBSE PMT 1997; BHU 2001]
  A)
  2          done clear
  B)
              3 done clear
  C)
              4 done clear
  D)
              5 done clear
  View Solution play_arrow

• question_answer21)
  If the radius of earth's orbit is made 1/4, the duration of an year will become  [BHU 1998; JIPMER 2001, 2002]
  A)
  8 times done clear
  B)
                4 times done clear
  C)
              1/8 times done clear
  D)
                1/4 times done clear
  View Solution play_arrow

• question_answer22)
  Planetary system in the solar system describes [DCE 1999]
  A)
  Conservation of energy done clear
  B)
              Conservation of linear momentum done clear
  C)
              Conservation of angular momentum done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer23)
  If mass of a satellite is doubled and time period remain constant the ratio of orbit in the two cases will be                                         [RPET 2000]
  A)
  1 : 2     done clear
  B)
              1 : 1 done clear
  C)
              1 : 3     done clear
  D)
              None of these done clear
  View Solution play_arrow

• question_answer24)
  The earth revolves round the sun in one year. If the distance between them becomes double, the new period of revolution will be                           [MP PET 2000]
  A)
  1/2 year done clear
  B)
                \[2\sqrt{2}\] years done clear
  C)
              4 years done clear
  D)
              8 years done clear
  View Solution play_arrow

• question_answer25)
  Kepler discovered                          [DCE 2000]
  A)
  Laws of motion done clear
  B)
              Laws of rotational motion done clear
  C)
              Laws of planetory motion done clear
  D)
              Laws of curvilinear motion done clear
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• question_answer26)
  In the solar system, which is conserved            [DCE 2001]
  A)
  Total Energy done clear
  B)
                K.E. done clear
  C)
              Angular Velocity          done clear
  D)
              Linear Momentum done clear
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• question_answer27)
  The maximum and minimum distances of a comet from the sun are \[8\times {{10}^{12}}\,m\] and \[1.6\times {{10}^{12}}\,m\]. If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s when it is farthest                         [Orissa 2001]
  A)
  12        done clear
  B)
              60 done clear
  C)
              112      done clear
  D)
              6 done clear
  View Solution play_arrow

• question_answer28)
  A body revolved around the sun 27 times faster then the earth what is the ratio of their radii [DPMT 2002]
  A)
  1/3       done clear
  B)
              1/9 done clear
  C)
              1/27     done clear
  D)
              1/4 done clear
  View Solution play_arrow

• question_answer29)
  The period of moon?s rotation around the earth is nearly 29 days. If moon?s mass were 2 fold, its present value and all other things remained unchanged, the period of moon?s rotation would be nearly [Kerala (Engg.) 2002]
  A)
              \[29\sqrt{2}\]days done clear
  B)
                \[29/\sqrt{2}\] days done clear
  C)
              29 × 2 days done clear
  D)
                29 days done clear
  View Solution play_arrow

• question_answer30)
  Two planets at mean distance \[{{d}_{1}}\] and \[{{d}_{2}}\] from the sun and their frequencies are n1 and n2 respectively then                                  [Kerala (Med.) 2002]
  A)
              \[n_{1}^{2}d_{1}^{2}={{n}_{2}}d_{2}^{2}\] done clear
  B)
                \[n_{2}^{2}d_{2}^{3}=n_{1}^{2}d_{1}^{3}\] done clear
  C)
              \[{{n}_{1}}d_{1}^{2}={{n}_{2}}d_{2}^{2}\] done clear
  D)
                \[n_{1}^{2}{{d}_{1}}=n_{2}^{2}{{d}_{2}}\] done clear
  View Solution play_arrow

• question_answer31)
  Which of the following astronomer first proposed that sun is static and earth rounds sun                                [AFMC 2002]
  A)
  Copernicus      done clear
  B)
              Kepler done clear
  C)
              Galileo done clear
  D)
                None done clear
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• question_answer32)
  The distance of a planet from the sun is 5 times the distance between the earth and the sun. The time period of the planet is                            [UPSEAT 2003]
  A)
              \[{{5}^{3/2}}\] years done clear
  B)
                \[{{5}^{2/3}}\] years done clear
  C)
              \[{{5}^{1/3}}\] years done clear
  D)
                \[{{5}^{1/2}}\] years done clear
  View Solution play_arrow

• question_answer33)
  A planet is revolving around the sun as shown in elliptical path                            [UPSEAT 2003] The correct option is 
  A)
  The time taken in travelling DAB is less than that for BCD done clear
  B)
              The time taken in travelling DAB is greater than that for BCD done clear
  C)
              The time taken in travelling CDA is less than that for ABC done clear
  D)
              The time taken in travelling CDA is greater than that for ABC done clear
  View Solution play_arrow

• question_answer34)
  In the previous question the orbital velocity of the planet will be minimum at [UPSEAT 2003; RPET 2002]
  A)
  A          done clear
  B)
              B done clear
  C)
              C         done clear
  D)
              D done clear
  View Solution play_arrow

• question_answer35)
  The radius of orbit of a planet is two times that of the earth. The time period of planet is [BHU 2003; CPMT 2004]
  A)
  4.2 years done clear
  B)
                2.8 years done clear
  C)
              5.6 years done clear
  D)
                8.4 years done clear
  View Solution play_arrow

• question_answer36)
  The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be [MP PET 2003]
  A)
  16 L     done clear
  B)
              64 L done clear
  C)
              \[\frac{L}{4}\] done clear
  D)
              4 L done clear
  View Solution play_arrow

• question_answer37)
  According to Kepler?s law the time period of a satellite varies with its radius as             [Orissa JEE 2003]
  A)
              \[{{T}^{2}}\propto {{R}^{3}}\] done clear
  B)
                \[{{T}^{3}}\propto {{R}^{2}}\] done clear
  C)
                \[{{T}^{2}}\propto (1/{{R}^{3}})\] done clear
  D)
                \[{{T}^{3}}\propto (1/{{R}^{2}})\] done clear
  View Solution play_arrow

• question_answer38)
  In planetary motion the areal velocity of position vector of a planet depends on angular velocity \[(\omega )\] and the distance of the planet from sun (r). If so the correct relation for areal velocity is    [EAMCET 2003]
  A)
              \[\frac{dA}{dt}\propto \omega r\] done clear
  B)
              \[\frac{dA}{dt}\propto {{\omega }^{2}}r\] done clear
  C)
              \[\frac{dA}{dt}\propto \omega {{r}^{2}}\] done clear
  D)
                \[\frac{dA}{dt}\propto \sqrt{\omega r}\] done clear
  View Solution play_arrow

• question_answer39)
   The ratio of the distances of two planets from the sun is 1.38. The ratio of their period of revolution around the sun is                                [Kerala PMT 2004]
  A)
  1.38     done clear
  B)
              \[{{1.38}^{3/2}}\] done clear
  C)
              \[{{1.38}^{1/2}}\] done clear
  D)
                \[{{1.38}^{3}}\] done clear
  E)
              \[{{1.38}^{2}}.\] done clear
  View Solution play_arrow

• question_answer40)
  Kepler's second law (law of areas) is nothing but a statement of                  [UPSEAT 2004]
  A)
  Work energy theorem done clear
  B)
              Conservation of linear momentum done clear
  C)
              Conservation of angular momentum done clear
  D)
              Conservation of energy done clear
  View Solution play_arrow

• question_answer41)
   In an elliptical orbit under gravitational force, in general                   [UPSEAT 2004]
  A)
  Tangential velocity is constant done clear
  B)
              Angular velocity is constant done clear
  C)
              Radial velocity is constant done clear
  D)
              Areal velocity is constant done clear
  View Solution play_arrow

• question_answer42)
   If a new planet is discovered rotating around Sun with the orbital radius double that of earth, then what will be its time period (in earth's days)                            [DCE 2004]
  A)
  1032    done clear
  B)
              1023 done clear
  C)
              1024    done clear
  D)
               1043 done clear
  View Solution play_arrow

• question_answer43)
  Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. \[F\propto 1/{{r}^{3}}\], but still remaining a central force. Then                     [UPSEAT 2002]
  A)
  Keplers law of areas still holds done clear
  B)
              Keplers law of period still holds done clear
  C)
              Keplers law of areas and period still hold done clear
  D)
              Neither the law of areas, nor the law of period still holds done clear
  View Solution play_arrow

• question_answer44)
   What does not change in the field of central force  [MP PMT 2004]
  A)
  Potential energy done clear
  B)
                Kinetic energy done clear
  C)
              Linear momentum       done clear
  D)
              Angular momentum done clear
  View Solution play_arrow

• question_answer45)
  The eccentricity of earth's orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is            [NCERT 1973]
  A)
  2.507   done clear
  B)
              1.033 done clear
  C)
              8.324   done clear
  D)
              1.000 done clear
  View Solution play_arrow

• question_answer46)
  The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as                                 [AMU 1995]
  A)
              \[4{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\] done clear
  B)
                \[8{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\] done clear
  C)
              \[12{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\] done clear
  D)
                \[16{{\pi }^{2}}{{R}^{3}}{{G}^{-1}}{{T}^{-2}}\] done clear
  View Solution play_arrow

• question_answer47)
  If orbital velocity of planet is given by \[v={{G}^{a}}{{M}^{b}}{{R}^{c}}\], then      [EAMCET 1994]
  A)
              \[a=1/3,\,b=1/3,\,c=-1/3\] done clear
  B)
              \[a=1/2,\,b=1/2,\,c=-1/2\] done clear
  C)
                \[a=1/2,\,b=-1/2,\,c=1/2\] done clear
  D)
              \[a=1/2,\,b=-1/2,\,c=-1/2\] done clear
  View Solution play_arrow

• question_answer48)
   Hubble's law states that the velocity with which milky way is moving away from the earth is proportional to [Kerala PMT 2004]
  A)
  Square of the distance of the milky way from the earth done clear
  B)
              Distance of milky way from the earth done clear
  C)
              Mass of the milky way done clear
  D)
              Product of the mass of the milky way and its distance from the earth done clear
  E)
              Mass of the earth done clear
  View Solution play_arrow

• question_answer49)
  Two satellite are revolving around the earth with velocities \[{{v}_{1}}\]and \[{{v}_{2}}\] and in radii \[{{r}_{1}}\] and \[{{r}_{2}}({{r}_{1}}>{{r}_{2}})\]respectively. Then [BHU 2005]
  A)
              \[{{v}_{1}}={{v}_{2}}\]     done clear
  B)
              \[{{v}_{1}}>{{v}_{2}}\] done clear
  C)
              \[{{v}_{1}}<{{v}_{2}}\]     done clear
  D)
              \[\frac{{{v}_{1}}}{{{r}_{1}}}=\frac{{{v}_{2}}}{{{r}_{2}}}\] done clear
  View Solution play_arrow

• question_answer50)
  The condition for a uniform spherical mass m of radius r to be a black hole is [G= gravitational constant and g= acceleration due to gravity]                        [AIIMS 2005]
  A)
              \[{{(2Gm/r)}^{1/2}}\le c\] done clear
  B)
                \[{{(2Gm/r)}^{1/2}}=c\] done clear
  C)
              \[{{(2Gm/r)}^{1/2}}\ge c\] done clear
  D)
                \[{{(gm/r)}^{1/2}}\ge c\] done clear
  View Solution play_arrow

• question_answer51)
  Earth is revolving around the sun if the distance of the Earth from the Sun is reduced to 1/4th of the present distance then the present day length reduced by                        [BHU 2005]
  A)
              \[\frac{1}{4}\] done clear
  B)
              \[\frac{1}{2}\] done clear
  C)
   \[\frac{1}{8}\]            done clear
  D)
   \[\frac{1}{6}\] done clear
  View Solution play_arrow