## JEE Main Previous Year Papers Questions With Solutions Physics Gravitation

Multiple Choice with ONE correct answer
1.If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would [1981-2 marks]
(a)decrease                                          (b)remain unchanged
(c) increase                                            (d) none of
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2.If g is the acceleration due to gravity on the earth’s surface, the gain in 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  [1983-1 mark]
(a)  1/2mgR                                (b)2 mgR
(c) mgR                                       (d)1/4 mgR
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3.If the distance between the earth and the sun were half its present value, the number of days in a year would have been       [1996-2 marks]
(a).64.5                                     (b) 129
(c) 182.5                                   (d) 730
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4.An artificial satellite moving in a circular orbit around the earth has total (K.E. + P.E.)energyE0. Its potential energy is                [1997-1 mark]
(a)- E0                       (b)1.5 E0
(c) 2 E0                       (d)E0
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5. A simple pendulum has a time period T1 when on the earth’s surface, and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T2/T1 is  [2001]
a)      1                                                              b) √2
c) 4                                                                  d) 2
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6. A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy satellite orbiting a few hundred km above the earth’s surface (Rg^ =6,400km) will approximately be                                                                         [2002]
a) (l/2)hr                                      b) 1 hr
c) 2 hr                                          d) 4 hr
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7.A Binary star system consists or two stars A and B which have time periods TA and TB, radii RA and RB and masses MA and MB. Then
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9.  A satellite is moving with a constant speed ‘V’ in a cirular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just < escapes from the gravitation pull of the earth. At the time of its ejection, the kinetic energy of the object is
(a)1/2 mV2                                            (b)mV2
(c) 3/2 mV2                                            (d)2 mV2
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10.  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 the planet and the star is proportional to R-5/2       [1989-2 marks]

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11.   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 (2,0,0) respectively, are taken out of the solid leaving behind spherical cavities as shown in fig. Then:      [1993-2 marks]

a)    the gravitational force due to this object at the origin is zero.
b)       the gravitational force at the point B (2,0,0) is zero.
c)    the gravitational potential is the same at all points of circle y2 + z2 = 36.
d)    the gravitational potential is the same at all points on the circle y2 + z2 = 4.
Ans.

a)Due to solid sphere of uniform density, gravitational field is zero at centre O. The cavities at A and B can be treated as negative masses. The cavities are situated on opposite sides of the centre O. The gravitational forces, exerted by the cavity- masses, on a mass at O are opposite. Hence the resultant force on mass at O is zero. Thus the gravitational force due to this object at the origin O is zero, option (a) is correct
b)Option (b) is incorrect in view of the above discussion. c)and (d)-These are correct options.
Consider the circle, y2 + z2 = 36 The centre of circle is (0,0,0). The radius of circle is 6 units.
The circle lies in (y-z) plane.lt is JL to x-axis. For a point situated on or outside the sphere, the mass of sphere can be assumed to be situated at the centre. All the points of circle y2 + z2 = 36 are equidistant from the centre O of the sphere, where the mass is supposed to be concentrated. Hence the gravitational potential is the same at all points of circle y2 + z2 = 36 Option (c) is correct.
Consider the circle y2 + z2 = 4.
Its centre lies at (0,0,0). Its radius is 2 units. It lies in y-Tf plane, perpendicular to x-axis A discussion on the lines of option (c) leads to the conclusion that (d) is a correct option.
Thus (c) and (d) represent correct options.
12. The magnitudes of the gravitational field at distances rt and r2 from the centre of a uniform sphere of radius R and mass m are F1 and F2 respectively. Then     [1994-2 marks]

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13   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 the earth. [1998-2 marks]
a)    The acceleration of S is always directed towards the centre of the earth.
b)    The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.
c)     The total mechanical energy of S varies periodically with time.
d)    The linear momentum of S remains constant in magnitude.
Ans.(a), (c) a) Force on satellite (S) of earth is always towards earth which attracts the satellite with the gravitational force. Hence the acceleration of S is always directed towards the centre of earth Option (a) is correct.
b)The torque of gravitational force about centre of earth is zero. Therefore, angular momentum remains constant in magnitude as well as direction .Option (b) is not correct
c)The gravitational force is conservative in nature. Mechanical energy of satellite, therefore, remains constant.The speed of satellite varies periodically as it varies with distance from earth. Speed of S is maximum when it is nearest to earth and minimum when it is farthest. Thus the mechanical energy of S varies periodically with time. Option (c) is thus correct.
d)Since the magnitude of velocity of S varies along its elliptic orbit, the linear momentum of S does not remain constant in magnitude. Option (d) is not correct.
14.A thin uniform annular disc (see figure) of mass M has outer rdius 4R and inner radius 3R. The work P on its axis to infinity is     [2010]

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Assertion & Reasoning type
Instructions : The following question contains statement-I (assertion) and statement -2 (reason). Of these statements, mark correct choice if
a)    Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)    Statements-1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)     Statement-1 is true, statement-2 is flase
d)    Statement-1 is false, statement-2 is true.
15.   Statement – 1 : An astronaut in an orbiting space station above the Earth experiences weightlessness.
Statement – 2 : An object moving around the Earth under the influence of Earth’s gravitational force is in
Ans.(a) If only the gravitational force of the Earth acts on the astronaut, (that, he is in a state of free fall), he will feel weightless. Statement-2 is a correct explanation of statement-1.
16. Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column H. Match the physical quantities in Column I with the units in Column II. [2007]

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Subjective/Numerical integer type
18.Two satellites St and S2 revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hour respectively. The radius of the orbit of S1 is 1okm. When S2 is closest to S1, find [1986-6 marks]
a)the speed of S2 relative to Sp
b)the angular speed of S2 as actually observed by an astronaut in SP
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19.Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces.lt is desired that each particle moves in a circle while maintaining the original mutual separation a. Find the initial velocity that should be given to each particle and also the time period of the circular motion. [1988-5 marks]
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20.An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth.[1990-8 marks]
i)Determine the height of the satellite above the earth’s surface.
ii)If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth, find the speed with which it hits the surface of the earth.
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21.Distance between the centres of two stars is 10 a. The masses of these stars are M and 16 M and their radii a and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the smaller star.What should be its minimum initial speed to reach the surface of the smaller star ? Obtain the expression in terms of G, M and a.   [1996-5 marks]
Ans.Let O1 denote the centre of smaller star Sj having radius (a) and mass (M)

22.A body is projected vertically upwards from the bottom of a crater of moon of depth R/100 where R is the radius of moon with a velocity equal to the escape velocity on the surface of moon. Calculate maximum height attained by the body from the surface of the moon. [2003-4 marks]
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True / False Type
23.It is possible to put an artificial satellite into orbit in such a way that it will always remain directly over New Delhi.   [1984- 2 marks]
Ans.(False) New Delhi is not on equatorial plane while the geo-stationary satellite is launched on the equa­torial plane. Hence the statement is false.

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Fill in the blanks
25.The numerical value of the angular velocity of rotation of the earth should be………… rad/s in order to make the effective acceleration due to gravity at equator equal to zero.   [1984-2 marks]
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26.According to Kepler’s second law, the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time. This lav/ is a consequence of the conservation of…………………. [1985-2 marks]
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27.A geo-stationary satellite is orbiting the earth at a height of 6R above the surface of the earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of the earth is………..hour [1987-2 marks]
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28.The masses and radii of the earth and the moon are Mp Rj and M2, R2 respectively. Their centres are at a distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is………………… [1988-2 marks]
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29.The ratio of earth’s orbital angular momentum (about the sun) to its mass is 4.4 x l015 m2/s. The area enclosed by earth’s orbit approximately is………  m2 [1997-1 mark]
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30.A particle is projected vertically upwards from the surface of earth (radius Re) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface of earth is………………….. [1997-2 marks]
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Courtesy : CBSE