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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)
\[{{R}^{\left( \frac{n-1}{2} \right)}}\] done
clear
C)
\[{{R}^{n}}\] done
clear
D)
\[{{R}^{\left( \frac{n-2}{2} \right)}}\] 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 [IIT-JEE 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 [IIT-JEE (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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