
question_answer1) Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to \[{{R}^{\frac{5}{2}}}\], then \[{{T}^{2}}\] is proportional to [IIT 1989; RPMT 1997]
A) \[{{R}^{3}}\] done
clear
B) \[{{R}^{7/2}}\] done
clear
C) \[{{R}^{5/2}}\] done
clear
D) \[{{R}^{3/2}}\] done
clear
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question_answer2) The magnitudes of the gravitational force at distances \[{{r}_{1}}\] and \[{{r}_{2}}\] from the centre of a uniform sphere of radius R and mass M are \[{{F}_{1}}\] and \[{{F}_{2}}\] respectively. Then [IIT 1994]
A) \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\] if \[{{r}_{1}}<R\] and \[{{r}_{2}}<R\] done
clear
B) \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{r_{1}^{2}}{r_{2}^{2}}\] if \[{{r}_{1}}>R\] and \[{{r}_{2}}>R\] done
clear
C) \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\] if \[{{r}_{1}}>R\] and \[{{r}_{2}}>R\] done
clear
D) \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{r_{2}^{2}}{r_{1}^{2}}\] if \[{{r}_{1}}<R\] and \[{{r}_{2}}<R\] done
clear
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question_answer3) A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth [IIT 1998]
A) The acceleration of S is always directed towards the centre of the earth done
clear
B) The angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant done
clear
C) The total mechanical energy of S varies periodically with time done
clear
D) The linear momentum of S remains constant in magnitude done
clear
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question_answer4) A mass M is split into two parts, m and (M?m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts [AMU 2000]
A) 1/3 done
clear
B) 1/2 done
clear
C) 1/4 done
clear
D) 1/5 done
clear
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question_answer5) Suppose the gravitational force varies inversely as the \[{{n}^{th}}\] power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004]
A) \[{{R}^{\left( \frac{n+1}{2} \right)}}\] done
clear
B) \[{{R}^{\left( \frac{n1}{2} \right)}}\] done
clear
C) \[{{R}^{n}}\] done
clear
D) \[{{R}^{\left( \frac{n2}{2} \right)}}\] done
clear
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question_answer6) If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would [IIT 1981; CPMT 1981; MP PMT 1996, 97; Roorkee 1992; MP PET 1999; Kerala PMT 2004]
A) Decrease by 2% done
clear
B) Remain unchanged done
clear
C) Increase by 2% done
clear
D) Increase by 1% done
clear
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question_answer7) The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth [Roorkee 2000]
A) g will increase done
clear
B) g will decrease done
clear
C) Escape velocity will remain unchanged done
clear
D) Potential energy will remain unchanged done
clear
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question_answer8) In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be \[(g=10\,m{{s}^{2}}\] and radius of earth is 6400 kms) [Roorkee 2000]
A) \[0\,\ rad\,{{\sec }^{1}}\] done
clear
B) \[\frac{1}{800}rad\,se{{c}^{1}}\] done
clear
C) \[\frac{1}{80}rad\,se{{c}^{1}}\] done
clear
D) \[\frac{1}{8}rad\,se{{c}^{1}}\] done
clear
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question_answer9) A simple pendulum has a time period \[{{T}_{1}}\] when on the earth?s surface and \[{{T}_{2}}\] when taken to a height R above the earth?s surface, where R is the radius of the earth. The value of \[{{T}_{2}}/{{T}_{1}}\] is [IITJEE 2001]
A) 1 done
clear
B) \[\sqrt{2}\] done
clear
C) 4 done
clear
D) 2 done
clear
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question_answer10) A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be [NCERT 1971; CPMT 1971, 97; IIT 1983; CBSE PMT 1991; Kurukshetra CEE 1996; CMEET Bihar 1995; MNR 1998; AIEEE 2004]
A) mgR done
clear
B) \[\frac{1}{2}mgR\] done
clear
C) 2 mgR done
clear
D) \[\frac{1}{4}mgR\] done
clear
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question_answer11) An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy \[{{E}_{0}}\]. Its potential energy is [IIT 1997 Cancelled; MH CET 2002; MP PMT 2000]
A) \[{{E}_{0}}\] done
clear
B) \[1.5\,{{E}_{0}}\] done
clear
C) \[2\,{{E}_{0}}\] done
clear
D) \[{{E}_{0}}\] done
clear
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question_answer12) A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is [AMU 1995]
A) \[R/\left( \frac{gR}{2{{V}^{2}}}1 \right)\] done
clear
B) \[R\,\left( \frac{gR}{2{{V}^{2}}}1 \right)\] done
clear
C) \[R/\left( \frac{2gR}{{{V}^{2}}}1 \right)\] done
clear
D) \[R\left( \frac{2gR}{{{V}^{2}}}1 \right)\] done
clear
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question_answer13) A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(? 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure [IIT 1993]
A) The gravitational force due to this object at the origin is zero done
clear
B) The gravitational force at the point B (2, 0, 0) is zero done
clear
C) The gravitational potential is the same at all points of the circle \[{{y}^{2}}+{{z}^{2}}=36\] done
clear
D) The gravitational potential is the same at all points on the circle \[{{y}^{2}}+{{z}^{2}}=4\] done
clear
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question_answer14) Two bodies of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is [BHU 1994; RPET 1999]
A) \[{{\left[ 2G\frac{({{m}_{1}}{{m}_{2}})}{r} \right]}^{1/2}}\] done
clear
B) \[{{\left[ \frac{2G}{r}({{m}_{1}}+{{m}_{2}} \right]}^{1/2}}\] done
clear
C) \[{{\left[ \frac{r}{2G({{m}_{1}}{{m}_{2}})} \right]}^{1/2}}\] done
clear
D) \[{{\left[ \frac{2G}{r}{{m}_{1}}{{m}_{2}} \right]}^{1/2}}\] done
clear
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question_answer15) A projectile is projected with velocity \[k{{v}_{e}}\] in vertically upward direction from the ground into the space. (\[{{v}_{e}}\] is escape velocity and \[k<1)\]. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth) [Roorkee 1999; RPET 1999]
A) \[\frac{R}{{{k}^{2}}+1}\] done
clear
B) \[\frac{R}{{{k}^{2}}1}\] done
clear
C) \[\frac{R}{1{{k}^{2}}}\] done
clear
D) \[\frac{R}{k+1}\] done
clear
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question_answer16) A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.01)R. The period of the second satellite is larger than that of the first one by approximately [IIT 1995]
A) 0.5% done
clear
B) 1.0% done
clear
C) 1.5% done
clear
D) 3.0% done
clear
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question_answer17) If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been [IIT 1996; RPET 1996]
A) 64.5 done
clear
B) 129 done
clear
C) 182.5 done
clear
D) 730 done
clear
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question_answer18) A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few hundred kilometres above the earth?s surface \[({{R}_{\text{Earth}}}=6400\,km)\] will approximately be [IITJEE (Screening) 2002]
A) 1/2 h done
clear
B) 1 h done
clear
C) 2 h done
clear
D) 4 h done
clear
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