JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank

done Self Evaluation Test - Gravitation Total Questions - 100

• question_answer1)
  Let \[\omega \] be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth's surface at a pole\[(d<<R)\]. The value of d is
  A)
  \[\frac{{{\omega }^{2}}{{R}^{2}}}{g}\] done clear
  B)
  \[\frac{{{\omega }^{2}}{{R}^{2}}}{2g}\] done clear
  C)
  \[\frac{2{{\omega }^{2}}{{R}^{2}}}{g}\] done clear
  D)
  \[\frac{\sqrt{Rg}}{g}\] done clear
  View Solution play_arrow

• question_answer2)
  In a gravitational field, at a point where the gravitational potential is zero
  A)
  the gravitational field is necessarily zero done clear
  B)
  the gravitational field is not necessarily zero done clear
  C)
  any value between one and infinite done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  The gravitational field strength due to a solid sphere (mass M, radius R) varies with distance r from centre as              
  A)
          done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer4)
  A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at \[\frac{a}{2}\] distance from the centre, will be:
  A)
  \[-\frac{3GM}{a}\]         done clear
  B)
         \[-\frac{2GM}{a}\] done clear
  C)
  \[-\frac{GM}{a}\]           done clear
  D)
         \[-\frac{4GM}{a}\] done clear
  View Solution play_arrow

• question_answer5)
  Assuming the radius of the earth as R, the change in gravitational potential energy of a body of mass m, when it is taken from the earth's surface to a height 3R above its surface, is
  A)
  \[3\text{ }mgR\] done clear
  B)
  \[\frac{3}{4}mgR\] done clear
  C)
  \[\text{1 }mgR\] done clear
  D)
  \[\frac{3}{2}mgR\] done clear
  View Solution play_arrow

• question_answer6)
  The figure shows a planet in elliptical orbit around the sun 5'. Where is the kinetic energy of the planet maximum?  
  A)
  \[{{P}_{1}}\] done clear
  B)
  \[{{P}_{2}}\]    done clear
  C)
  \[{{P}_{3}}\] done clear
  D)
  \[{{P}_{4}}\] done clear
  View Solution play_arrow

• question_answer7)
  A planet revolves about the sun in elliptical orbit. The areal velocity \[\left( \frac{dA}{dt} \right)\] of the planet is\[4.0\times 1{{0}^{16}} m/s\]. The least distance between planet and the sun is\[2\times {{10}^{12}}m\]. Then the maximum speed of the planet in km/s is
  A)
  10 done clear
  B)
  20    done clear
  C)
  30 done clear
  D)
  40 done clear
  View Solution play_arrow

• question_answer8)
  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
  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_answer9)
  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 remain unchanged, the period of moon's rotation would be nearly
  A)
  \[29\sqrt{2} days\] done clear
  B)
  \[29/\sqrt{2} days\] done clear
  C)
  \[29\times 2 days\] done clear
  D)
  29 days done clear
  View Solution play_arrow

• question_answer10)
  Which of the following graphs represents the moon planet moving about the sun?
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer11)
  If three equal masses m are placed at the three vertices of an equilateral triangle of side \lm then what force acts on a particle of mass 2m placed at the centroid?
  A)
  \[G{{m}^{2}}\] done clear
  B)
  \[2G{{m}^{2}}\] done clear
  C)
  Zero      done clear
  D)
  \[-G{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer12)
  Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is
  A)
  \[\sqrt{\frac{Gm}{4R}}\] done clear
  B)
  \[\sqrt{\frac{Gm}{3R}}\] done clear
  C)
  \[\sqrt{\frac{Gm}{2R}}\] done clear
  D)
  \[\sqrt{\frac{Gm}{R}}\] done clear
  View Solution play_arrow

• question_answer13)
  If suddenly the gravitational force of attraction between Earth and a body revolving around it becomes zero, then the body will
  A)
  Continue to move in its orbit with same velocity done clear
  B)
  Move tangentially to the original orbit with same velocity done clear
  C)
  Become stationary in its orbit done clear
  D)
  Move towards the earth done clear
  View Solution play_arrow

• question_answer14)
  A straight rod of length L extends from \[x=a\]to\[x=L+a\]. Find the gravitational force it exerts on a point mass m at x = 0 if the linear density of rod\[\mu =A+B{{x}^{2}}\].                                              
  A)
  \[Gm\left[ \frac{A}{a}+BL \right]\] done clear
  B)
  \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]\] done clear
  C)
  \[Gm\left[ BL+\frac{A}{a+L} \right]\] done clear
  D)
  \[Gm\left[ BL+\frac{A}{a} \right]\] done clear
  View Solution play_arrow

• question_answer15)
  Two concentric uniform shells of mass \[{{M}_{1}}\] and \[{{M}_{2}}\] are as shown in the figure. A particle of mass m is located just within the shell \[{{M}_{2}}\] on its inner surface. Gravitational force on 'm' due to \[{{M}_{1}}\] and \[{{M}_{2}}\] will be
  A)
  Zero      done clear
  B)
  \[\frac{G{{M}_{1}}m}{{{b}^{2}}}\] done clear
  C)
    \[\frac{G\left( {{M}_{1}}+{{M}_{2}} \right)m}{{{b}^{2}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If \[{{t}_{1}}\] is the time for the planet to move from C to D and \[{{t}_{2}}\] is the time to move from A to B then
  A)
  \[{{t}_{i}}=4{{t}_{2}}\] done clear
  B)
  \[{{t}_{i}}=2{{t}_{2}}\] done clear
  C)
  \[{{t}_{i}}={{t}_{2}}\] done clear
  D)
  \[{{t}_{i}}>{{t}_{2}}\] done clear
  View Solution play_arrow

• question_answer17)
  If the distance of earth is halved from the sun, then the no. of days in a year will be
  A)
  365 done clear
  B)
  182.5 done clear
  C)
  730 done clear
  D)
  129 done clear
  View Solution play_arrow

• question_answer18)
  If the earth is at one-fourth of its present distance from the sun, the duration of the year will be
  A)
  half the present year done clear
  B)
  one-eighth the present year done clear
  C)
  one-sixth the present year done clear
  D)
  one-tenth the present year done clear
  View Solution play_arrow

• question_answer19)
  The distance of Neptune and Saturn from the sun is nearly \[1{{0}^{13}} and 1{{0}^{12}}\] meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio
  A)
  10 done clear
  B)
  100   done clear
  C)
  \[10\sqrt{10}\] done clear
  D)
  1000 done clear
  View Solution play_arrow

• question_answer20)
  A satellite A of mass m is at a distance of r from the surface 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
  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_answer21)
  The time taken by the earth to travel over half its orbit, remote from the sun, separated by the minor axis is about 2 days more than half the year, then the eccentricity of the orbit is
  A)
  1/30 done clear
  B)
  1/60  done clear
  C)
  1/15 done clear
  D)
  1/70 done clear
  View Solution play_arrow

• question_answer22)
  For a particle inside a uniform spherical shell, the gravitational force on the particle is
  A)
  Infinite done clear
  B)
  zero done clear
  C)
  \[\frac{-G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] done clear
  D)
  \[\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] done clear
  View Solution play_arrow

• question_answer23)
  Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
  A)
  \[\frac{F}{9}\] done clear
  B)
  3F    done clear
  C)
  F done clear
  D)
  \[\frac{F}{3}\] done clear
  View Solution play_arrow

• question_answer24)
  A mass M is split into two parts m and (M- w), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts?
  A)
  \[\frac{1}{3}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer25)
  Two stars of mass \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]are parts of a binary system. The radii of their orbits are \[{{r}_{1}} and {{r}_{2}}\]respectively, measured from the C.M. of the system. The magnitude of gravitational force \[{{\operatorname{m}}_{1}}\]exerts on \[{{m}_{2}}\]is
  A)
  \[\frac{{{m}_{1}}{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] done clear
  B)
  \[\frac{{{m}_{1}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] done clear
  C)
  \[\frac{{{m}_{2}}G}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] done clear
  D)
  \[\frac{\left( {{m}_{1}}+{{m}_{2}} \right)}{{{\left( {{r}_{1}}+{{r}_{2}} \right)}^{2}}}\] done clear
  View Solution play_arrow

• question_answer26)
  Two bodies of masses 4 kg and 9 kg are separated by a distance of 60 cm. A 1 kg mass is placed in between these two masses. If the net force on 1 kg is zero, then its distance from 4 kg mass is
  A)
  26 cm done clear
  B)
  30 cm done clear
  C)
  28 cm done clear
  D)
  24 cm done clear
  View Solution play_arrow

• question_answer27)
  If masses of two point objects is doubled and distance between them is tripled, then gravitational force of attraction between them will nearly
  A)
  Increase by 225% done clear
  B)
        decrease by 44% done clear
  C)
  Decrease by 56% done clear
  D)
         increase by 125% done clear
  View Solution play_arrow

• question_answer28)
  A central particle M is surrounded by a square array of other particles, separated by either distance d or distance d/2 along the perimeter of the square. The magnitude of the gravitational force on the central particle due to the other particles is
  A)
  \[\frac{9GMm}{{{d}^{2}}}\]   done clear
  B)
         \[\frac{5GMm}{{{d}^{2}}}\]  done clear
  C)
  \[\frac{3GMm}{{{d}^{2}}}\]   done clear
  D)
         \[\frac{GMm}{{{d}^{2}}}\] done clear
  View Solution play_arrow

• question_answer29)
  Three particles P, Q and R are placed as per given figure. Masses of P, Q and R are \[\sqrt{3}m,\,\,\sqrt{3}m\] and m respectively. The gravitational force on a fourth particle S of mass m is equal to
  A)
  \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in ST direction only done clear
  B)
  \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SQ direction and \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SU direction done clear
  C)
  \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]  in SQ direction only done clear
  D)
   \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\]in SQ direction and \[\frac{\sqrt{3}G{{M}^{2}}}{2{{d}^{2}}}\] in ST direction done clear
  View Solution play_arrow

• question_answer30)
  The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?
  A)
  \[\frac{2}{3}m\] done clear
  B)
  \[\frac{2}{9}m\] done clear
  C)
  18 m done clear
  D)
  6 m done clear
  View Solution play_arrow

• question_answer31)
  Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If \[{{\operatorname{R}}_{e}}\]is the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection                                                
  A)
  \[0.2{{\operatorname{R}}_{e}}\] done clear
  B)
  \[2{{\operatorname{R}}_{e}}\]  done clear
  C)
  \[0.5{{\operatorname{R}}_{e}}\] done clear
  D)
  \[5{{\operatorname{R}}_{e}}\] done clear
  View Solution play_arrow

• question_answer32)
  The height of the point vertically above the earth's surface, at which acceleration due to gravity becomes 1 % of its value at the earth's surface is (Radius of the earth = R)
  A)
  8 R       done clear
  B)
  9 R   done clear
  C)
  10 R done clear
  D)
  20 R done clear
  View Solution play_arrow

• question_answer33)
  The speed of earth's rotation about its axis is cd. Its speed is increases to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is:
  A)
  1 done clear
  B)
  8.5    done clear
  C)
  17 done clear
  D)
  34 done clear
  View Solution play_arrow

• question_answer34)
  A particle is suspended from a spring and it stretches the spring by 1 cm on the surface of earth. By how much amount the same particle will stretch the same spring at a place 800 km above the surface of earth.
  A)
  1.59 cm done clear
  B)
  2.38 cm done clear
  C)
  0.79 cm done clear
  D)
  1.38 cm done clear
  View Solution play_arrow

• question_answer35)
  The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be-
  A)
  1/2 R done clear
  B)
  2 R   done clear
  C)
  4 R  done clear
  D)
  ¼ R done clear
  View Solution play_arrow

• question_answer36)
  Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g?, then
  A)
  \[g'=g/9\] done clear
  B)
  \[g'=27g\] done clear
  C)
  \[g=9g\] done clear
  D)
  \[g'=3g\] done clear
  View Solution play_arrow

• question_answer37)
  If the earth were to rotates faster than its present speed, the weight of an object will
  A)
  Increase at the equator but remain unchanged at the poles done clear
  B)
  Decrease at the equator but remain unchanged at the poles done clear
  C)
  Remain unchanged at the equator but decrease at the poles done clear
  D)
  Remain unchanged at the equator but increase at the poles done clear
  View Solution play_arrow

• question_answer38)
  Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Then, velocity of a particle is given by
  A)
  \[{{\left[ \frac{Gm}{r}\left( \frac{1+2\sqrt{2}}{4} \right) \right]}^{\frac{1}{2}}}\]             done clear
  B)
  \[\sqrt{\frac{Gm}{r}}\] done clear
  C)
  \[\sqrt{\frac{Gm}{r}}\left( 1+2\sqrt{2} \right)\]     done clear
  D)
  \[a{{\left[ \frac{1}{2}\frac{Gm}{r}\left( \frac{1+2\sqrt{2}}{2} \right) \right]}^{\frac{1}{2}}}\] done clear
  View Solution play_arrow

• question_answer39)
  Consider two solid uniform spherical objects of the same density p. One has radius R and the other has radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?                    
  A)
          \[G{{\pi }^{2}}{{R}^{2}}\] done clear
  B)
  \[\frac{128}{81}G{{\pi }^{2}}{{R}^{4}}{{\rho }^{2}}\] done clear
  C)
  \[\frac{128}{81}G{{\pi }^{2}}\] done clear
  D)
  \[\frac{128}{81}{{\pi }^{2}}{{R}^{4}}G\] done clear
  View Solution play_arrow

• question_answer40)
  Two spherical bodies of mass M and 5M& radii R & 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
  A)
  2.5 R done clear
  B)
  4.5 R done clear
  C)
  7.5 R done clear
  D)
  1.5 R done clear
  View Solution play_arrow

• question_answer41)
  From a sphere of mass M and radius R, a smaller sphere of radius \[\frac{R}{2}\] is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is
  A)
  \[\frac{41\,G{{M}^{2}}}{3600\,{{R}^{2}}}\] done clear
  B)
   \[\frac{41\,G{{M}^{2}}}{450\,{{R}^{2}}}\] done clear
  C)
   \[\frac{59\,G{{M}^{2}}}{450\,{{R}^{2}}}\] done clear
  D)
  \[\frac{G{{M}^{2}}}{225\,{{R}^{2}}}\] done clear
  View Solution play_arrow

• question_answer42)
  The value of acceleration due to gravity on moving from equator to poles will
  A)
  Decrease done clear
  B)
  increase done clear
  C)
  Remain same done clear
  D)
  become half done clear
  View Solution play_arrow

• question_answer43)
  The weight of a body at the centre of the earth is
  A)
  Zero done clear
  B)
  Infinite done clear
  C)
  Same as on the surface of earth done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer44)
  Which of the following graphs shows the correct variation of acceleration due to gravity with the height above the earth's surface?            
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer45)
  At what height from the ground will the value of g be the same as that in 10 km deep mine below the surface of earth?
  A)
  20 km   done clear
  B)
         10 km done clear
  C)
  15 km   done clear
  D)
         5 km done clear
  View Solution play_arrow

• question_answer46)
  The ratio of radii of earth to another planet is 21 3 and the ratio of their mean densities is 4/5. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is
  A)
  1 m       done clear
  B)
         0.8 m done clear
  C)
  0.5 m    done clear
  D)
         125 m done clear
  View Solution play_arrow

• question_answer47)
  The value of 'g' at a particular point is\[9.8 m/{{s}^{2}}\]. Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass. The value of 'g? at the same point (assuming that the distance of the point from the centre of the earth does not shrink) will now be
  A)
  \[4.9\,\,m/se{{c}^{2}}\] done clear
  B)
  \[3.1\,\,m/se{{c}^{2}}\] done clear
  C)
  \[9.8\,\,m/se{{c}^{2}}\] done clear
  D)
  \[19.6\,\,m/se{{c}^{2}}\] done clear
  View Solution play_arrow

• question_answer48)
  R is the radius of the earth and co is its angular velocity and \[{{\operatorname{g}}_{p}}\]is the value of g at the poles. The effective value of g at the latitude \[\lambda = 60{}^\circ \] will be equal to
  A)
  \[{{g}_{p}}-\frac{1}{4}R{{\omega }^{2}}\]      done clear
  B)
  \[{{g}_{p}}-\frac{3}{4}R{{\omega }^{2}}\] done clear
  C)
  \[{{g}_{p}}-R{{\omega }^{2}}\] done clear
  D)
  \[{{g}_{p}}+\frac{1}{4}R{{\omega }^{2}}\] done clear
  View Solution play_arrow

• question_answer49)
  What should be the velocity of rotation of earth due to rotation about its own axis so that the weight of a person becomes \[\frac{2}{3}\] of the present weight at the equator? Equatorial radius of the earth is R
  A)
  \[{{\left( \frac{2g}{3R} \right)}^{\frac{1}{2}}}\] done clear
  B)
  \[{{\left( \frac{g}{3R} \right)}^{\frac{1}{2}}}\] done clear
  C)
  \[{{\left( \frac{g}{7R} \right)}^{\frac{1}{2}}}\] done clear
  D)
  \[{{\left( \frac{g}{5R} \right)}^{\frac{1}{2}}}\] done clear
  View Solution play_arrow

• question_answer50)
  If the radius of the earth were to shrink by 1 %, with its mass remaining the same, the acceleration due to gravity on the earth's surface would
  A)
  Decrease by 1% done clear
  B)
  decrease by 2% done clear
  C)
  Increase by 1% done clear
  D)
  increase by 2% done clear
  View Solution play_arrow

• question_answer51)
  While approaching a planet circling a distant star, an astronaut determines the radius of a planet is half of that of the earth. After landing on its surface, he finds its acceleration due to gravity is twice as that of the earth. The ratio of the mass of planet and that of the earth.
  A)
  1 :2 done clear
  B)
  2:3 done clear
  C)
  3:4 done clear
  D)
  4:5 done clear
  View Solution play_arrow

• question_answer52)
  The depth d at which the value of acceleration due to gravity becomes \[\frac{1}{n}\] times the value at the surface of the earth, is [R = radius of the earth]
  A)
  \[\frac{R}{n}\] done clear
  B)
  \[R\left( \frac{n-1}{n} \right)\] done clear
  C)
  \[\frac{R}{{{n}^{2}}}\] done clear
  D)
  \[R\left( \frac{n}{n+1} \right)\] done clear
  View Solution play_arrow

• question_answer53)
  The radii of two planets are respectively \[{{R}_{1}}\] and \[{{R}_{2}}\] their densities are respectively\[{{\rho }_{1}} and {{\rho }_{2}}\]. The ratio of the accelerations due to gravity at their surfaces is       
  A)
  \[{{g}_{1}}:{{g}_{2}}=\frac{{{\rho }_{1}}}{{{R}_{1}}^{2}}:\frac{{{\rho }_{2}}}{{{R}_{2}}^{2}}\] done clear
  B)
  \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{\rho }_{1}}{{\rho }_{2}}\] done clear
  C)
  \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{R}_{2}}{{\rho }_{1}}\] done clear
  D)
  \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{\rho }_{1}}:{{R}_{2}}{{\rho }_{2}}\] done clear
  View Solution play_arrow

• question_answer54)
  The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon\[=7.36\times 1{{0}^{22}} kg\], radius of the moon's orbit\[= 3.8\times 1{{0}^{8}} m\]).
  A)
  \[6.73\times 1{{0}^{-5}} m/{{s}^{2}}\] done clear
  B)
  \[6.73\times 1{{0}^{-3}} m/{{s}^{2}}\] done clear
  C)
  \[6.73\times 1{{0}^{-2}} m/{{s}^{2}}\] done clear
  D)
  \[6.73\times 1{{0}^{-4}} m/{{s}^{2}}\] done clear
  View Solution play_arrow

• question_answer55)
  Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth\[={{\operatorname{R}}_{E}}\])
  A)
  done clear
  B)
         done clear
  C)
        done clear
  D)
  done clear
  View Solution play_arrow

• question_answer56)
  Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then
  A)
  g decreases by 2% and K decreases by 4% done clear
  B)
  g decreases by 4% and K increases by 2% done clear
  C)
  g increases by 4% and K decreases by 4% done clear
  D)
  g decreases by 4% and K increases by 4% done clear
  View Solution play_arrow

• question_answer57)
  Two concentric spherical shells are as shown in figure. Choose the correct statement given below.
  A)
  Potential at A is greater than B done clear
  B)
  Gravitational field at A is less than B done clear
  C)
  As one moves from C to D then potential remains constant done clear
  D)
  As one moves from D to A then gravitational field decreases done clear
  View Solution play_arrow

• question_answer58)
  The potential energy of a rock, having mass m and rotating at a height of\[3.2\times {{10}^{6}}m\] from the earth surface, is
  A)
  \[-6\,\,mg{{R}_{e}}\] done clear
  B)
  \[-0.67\,\,mg{{R}_{e}}\] done clear
  C)
  \[-0.99\,\,mg{{R}_{e}}\] done clear
  D)
  \[-0.33\,\,mg{{R}_{e}}\] done clear
  View Solution play_arrow

• question_answer59)
  Intensity of the gravitational field inside the hollow spherical shell is
  A)
  Variable done clear
  B)
  minimum done clear
  C)
  Maximum done clear
  D)
  zero done clear
  View Solution play_arrow

• question_answer60)
  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
  A)
  \[\frac{1}{4}mgr\] done clear
  B)
  \[\frac{1}{2}mgr\] done clear
  C)
  \[2\,mgr\] done clear
  D)
  \[mgr\] done clear
  View Solution play_arrow

• question_answer61)
  Radius of moon is 1/4 times that of earth and mass is 1/81 times that of earth. The point at which gravitational field due to earth becomes equal and opposite to that of moon, is (Distance between centres of earth and moon is 60R, where R is radius of earth)
  A)
  5.75 R from centre of moon done clear
  B)
  16 R from surface of moon done clear
  C)
  53 R from centre of earth done clear
  D)
  54 R from centre of earth done clear
  View Solution play_arrow

• question_answer62)
  Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have
  A)
  (a)\[V=O\text{ }and\text{ }E=0\] done clear
  B)
  \[\operatorname{V}=0 and E\ne 0\] done clear
  C)
  \[\operatorname{V}\ne 0 and E=0\] done clear
  D)
  All of the above done clear
  View Solution play_arrow

• question_answer63)
  A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre
  A)
  Increases done clear
  B)
  decreases done clear
  C)
  remains constant done clear
  D)
  cannot say done clear
  View Solution play_arrow

• question_answer64)
  The gravitational potential at the centre of a square of side 'a? and four equal masses (m each) placed at the comers of a square is
  A)
  Zero done clear
  B)
  \[4\sqrt{2}\frac{Gm}{a}\] done clear
  C)
  \[-4\sqrt{2}\frac{Gm}{a}\] done clear
  D)
  \[-4\sqrt{2}\frac{G{{m}^{2}}}{a}\] done clear
  View Solution play_arrow

• question_answer65)
  Three identical stars, each of mass M, form an equilateral triangle (stars are positioned at the comers) that rotates around the centre of-the triangle. The system is isolated and edge length of the triangle is L. The amount of work done, that is required to dismantle the system is:
  A)
  (a)\[\frac{3G{{M}^{2}}}{L}\] done clear
  B)
  \[\frac{3G{{M}^{2}}}{2L}\] done clear
  C)
  \[\frac{3G{{M}^{2}}}{4L}\] done clear
  D)
  \[\frac{G{{M}^{2}}}{2L}\] done clear
  View Solution play_arrow

• question_answer66)
  Inside a uniform sphere of density p there is a spherical cavity whose centre is at a distance \[\ell \]from the centre of the sphere. Find the strength F of the gravitational field inside the cavity at the point P.                                                  
  A)
  \[\frac{4}{3}G\pi \rho \vec{\ell }\] done clear
  B)
  \[\frac{1}{3}G\pi \rho \vec{\ell }\] done clear
  C)
  \[\frac{2}{3}G\pi \rho \vec{\ell }\] done clear
  D)
  \[\frac{1}{2}G\pi \rho \vec{\ell }\] done clear
  View Solution play_arrow

• question_answer67)
  The work done required to increase the separation distance from \[{{\operatorname{x}}_{1}} to {{x}_{1}}+d\]between two masses \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]is
  A)
  \[\frac{G{{m}_{1}}{{m}_{2}}d}{{{x}_{1}}\left( {{x}_{1}}+d \right)}\] done clear
  B)
  \[\frac{G{{m}_{1}}{{m}_{2}}{{x}_{1}}}{\left( {{x}_{1}}+d \right)d}\] done clear
  C)
  \[\frac{-G{{m}_{1}}{{m}_{2}}{{x}_{1}}}{\left( {{x}_{1}}+d \right)}\] done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer68)
  Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length \[\ell \]is
  A)
  \[\frac{Gm}{{{\ell }^{2}}}\operatorname{along}+x-axis\]           done clear
  B)
  \[\frac{Gm}{\pi {{\ell }^{2}}}\operatorname{along}+y-axis\] done clear
  C)
  \[\frac{2\pi Gm}{{{\ell }^{2}}}\operatorname{along}+x-axis\] done clear
  D)
  \[\frac{2\pi Gm}{{{\ell }^{2}}}\operatorname{along}+y-axis\] done clear
  View Solution play_arrow

• question_answer69)
  In a certain region of space, gravitational field is given by\[I=-(K/r)\]. Taking the reference point to be at \[r={{r}_{0}}\]with \[V={{V}_{0}},\] find the potential.
  A)
  \[K\,\log \frac{r}{{{r}_{0}}}+{{V}_{0}}\] done clear
  B)
  \[K\,\log \frac{{{r}_{0}}}{r}+{{V}_{0}}\] done clear
  C)
  \[K\,\log \frac{r}{{{r}_{0}}}-{{V}_{0}}\] done clear
  D)
  \[\log \frac{{{r}_{0}}}{r}-{{V}_{0}}r\] done clear
  View Solution play_arrow

• question_answer70)
  A point P lies on the axis of a fixed ring of mass M and radius R, at a distance 2R from its centre O. A small particle starts from P and reaches O under gravitational attraction only. Its speed at O will be
  A)
  Zero done clear
  B)
  \[\sqrt{\frac{2Gm}{R}}\] done clear
  C)
  \[\sqrt{\frac{2Gm}{R}\left( \sqrt{5}-1 \right)}\] done clear
  D)
  \[\sqrt{\frac{2Gm}{R}\left( 1-\frac{1}{\sqrt{5}} \right)}\] done clear
  View Solution play_arrow

• question_answer71)
  The gravitational field, due to the 'left over part* of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly):
  A)
  \[\frac{5}{6}\frac{GM}{{{x}^{2}}}\] done clear
  B)
  \[\frac{8}{9}\frac{GM}{{{x}^{2}}}\] done clear
  C)
  \[\frac{7}{8}\frac{GM}{{{x}^{2}}}\] done clear
  D)
  \[\frac{6}{7}\frac{GM}{{{x}^{2}}}\] done clear
  View Solution play_arrow

• question_answer72)
  A space vehicle approaching a planet has a speed v, when it is very far from the planet. At that moment tangent of its trajectory would miss the centre of the planet by distance R. If the planet has mass M and radius r, what is the smallest value of R in order that the resulting orbit of the space vehicle will just miss the surface of the planet?
  A)
  \[\frac{r}{v}{{\left[ {{v}^{2}}+\frac{2GM}{r} \right]}^{\frac{1}{2}}}\]            done clear
  B)
  \[\operatorname{vr}\left[ 1+\frac{2GM}{r} \right]\] done clear
  C)
  \[\frac{r}{v}\left[ {{v}^{2}}+\frac{2GM}{r} \right]\]       done clear
  D)
  \[\frac{2GMv}{r}\] done clear
  View Solution play_arrow

• question_answer73)
  A sky lab of mass m kg is first launched from the surface of the earth in a circular orbit of radius 2R (from the centre of the earth) and then it is shifted form this circular orbit of radius 3R. The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are
  A)
  \[\frac{3}{4}\operatorname{mgR}, \frac{mgR}{6}\] done clear
  B)
  \[\frac{3}{4}\operatorname{mgR}, \frac{mgR}{12}\] done clear
  C)
  \[\operatorname{mgR}, mgR\]                  done clear
  D)
  \[2\operatorname{mgR}, mgR\] done clear
  View Solution play_arrow

• question_answer74)
  With what minimum speed should m be projected from point C in presence of two fixed masses M each at A and B as shown in the figure such that mass m should escape the gravitational attraction  of A and B
  A)
  \[\sqrt{\frac{2GM}{R}}\] done clear
  B)
  \[\sqrt{\frac{2\sqrt{2}GM}{R}}\] done clear
  C)
  \[2\sqrt{\frac{GM}{R}}\] done clear
  D)
  \[2\sqrt{2}\sqrt{\frac{GM}{R}}\] done clear
  View Solution play_arrow

• question_answer75)
  An artificial satellite is first taken to a height equal to half the radius of earth. Assume that it is at rest on the earth's surface initially and that it is at rest at this height. Let \[{{E}_{1}}\]be the energy required. It is then given the appropriate orbital speed such that it goes in a circular orbit at that height. Let E be the energy required. The ratio \[\frac{{{E}_{1}}}{{{E}_{2}}}\] is
  A)
  4:1 done clear
  B)
  3:1   done clear
  C)
  1:1 done clear
  D)
  1:2 done clear
  View Solution play_arrow

• question_answer76)
  A satellite is launched in the equatorial plane in such a way that it can transmit signals up to \[60{}^\circ \] latitude on the earth. The angular velocity of the satellite is
  A)
  \[\sqrt{\frac{GM}{8{{R}^{3}}}}\] done clear
  B)
  \[\sqrt{\frac{GM}{2{{R}^{3}}}}\] done clear
  C)
  \[\sqrt{\frac{GM}{4{{R}^{3}}}}\] done clear
  D)
  \[\sqrt{\frac{3\sqrt{3}GM}{8{{R}^{3}}}}\] done clear
  View Solution play_arrow

• question_answer77)
  A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
  A)
  \[\frac{g{{R}^{2}}}{R+x}\] done clear
  B)
  \[\frac{g{{R}^{2}}}{R-x}\] done clear
  C)
  \[gx\] done clear
  D)
  \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\] done clear
  View Solution play_arrow

• question_answer78)
  For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required?
  A)
  41% done clear
  B)
  61% done clear
  C)
  81% done clear
  D)
  98% done clear
  View Solution play_arrow

• question_answer79)
  The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. What will be the change in escape velocity?
  A)
  Increased by 2% done clear
  B)
  Decreased by 4% done clear
  C)
  Increased by 6% done clear
  D)
  Decreased by 8% done clear
  View Solution play_arrow

• question_answer80)
  A satellite of mass m is orbiting the earth in a circular orbit of radius R. It starts losing energy due to small air resistance at the rate of C J/s. Find the time taken for the satellite to reach the earth.
  A)
  \[\frac{GMm}{C}\left[ \frac{1}{R}-\frac{1}{r} \right]\] done clear
  B)
  \[\frac{GMm}{2C}\left[ \frac{1}{R}+\frac{1}{r} \right]\] done clear
  C)
  \[\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]\] done clear
  D)
  \[\frac{2GMm}{C}\left[ \frac{1}{R}+\frac{1}{r} \right]\] done clear
  View Solution play_arrow

• question_answer81)
  Two spheres each of mass M are situated at a distance 2d (see figure). A particle of mass \[m(m<<M)\]is taken along the path shown in figure. The work done in the process from A to B is
  A)
  \[\frac{7GMm}{d}\] done clear
  B)
  \[\frac{8GMm}{d}\] done clear
  C)
  \[-\frac{8GMm}{d}\] done clear
  D)
  zero done clear
  View Solution play_arrow

• question_answer82)
  An asteroid of mass m is approaching earth initially at a distance of\[10{{\operatorname{R}}_{e}}\], with speed\[{{v}_{i}}\]. It hits the earth with a speed \[{{v}_{f}}({{\operatorname{R}}_{e}}\,\,and\,\,{{M}_{e}}\], are radius and mass of earth), then    
  A)
   \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\]                       done clear
  B)
  \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1+\frac{1}{10} \right)\] done clear
  C)
  \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]             done clear
  D)
  \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\] done clear
  View Solution play_arrow

• question_answer83)
  In older times, people used to think that the earth was flat. Imagine that the earth is indeed not a sphere of radius R, but an infinite plate of thickness H. What value of is needed to allow the same gravitational acceleration to be experienced as on the surface of the actual earth? (Assume that the earth's density is uniform and equal in the two models
  A)
  2R/3 done clear
  B)
  4R/3 done clear
  C)
  8R/3 done clear
  D)
  R/3 done clear
  View Solution play_arrow

• question_answer84)
  A shell is fired vertically from the earth with speed \[\frac{{{V}_{esc}}}{N},\] where Nis some number greater than one and V is escape speed for the earth. Neglecting the nation of the earth and air resistance, the maximum altitude attained by the shell will be is radius of the earth)                      
  A)
  \[\frac{{{N}^{2}}{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] done clear
  B)
  \[\frac{N{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] done clear
  C)
  \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\] done clear
  D)
  \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}}\] done clear
  View Solution play_arrow

• question_answer85)
  A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is v. Due to the rotation of planet about its axis the acceleration due to gravity g at equator is 1/2 of g at poles. The escape velocity of a particle on the pole of planet in terms of v is
  A)
  \[{{v}_{e}}=2v\] done clear
  B)
  \[{{v}_{e}}=v\] done clear
  C)
  \[{{v}_{e}}=v/2\] done clear
  D)
  \[{{v}_{e}}=\sqrt{3}v\] done clear
  View Solution play_arrow

• question_answer86)
  The acceleration due to gravity on the surface of the moon is 1/6 that on the surface of earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities on earth and moon will be
  A)
  \[\frac{\sqrt{6}}{2}\] done clear
  B)
  \[\sqrt{24}\] done clear
  C)
  3 done clear
  D)
  \[\frac{\sqrt{3}}{2}\] done clear
  View Solution play_arrow

• question_answer87)
  Three equal masses (each m) are placed at the comers of an equilateral triangle of side 'a? Then the escape velocity of an object from the circumcentre P of triangle is:
  A)
  \[\sqrt{\frac{2\sqrt{3}Gm}{a}}\] done clear
  B)
  \[\sqrt{\frac{\sqrt{3}Gm}{a}}\]  done clear
  C)
  \[\sqrt{\frac{6\sqrt{3}Gm}{a}}\] done clear
  D)
  \[\sqrt{\frac{3\sqrt{3}Gm}{a}}\] done clear
  View Solution play_arrow

• question_answer88)
  A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface \[({{R}_{earth}} = 6,400km)\]will approximately be
  A)
  1/2hr done clear
  B)
  1hr   done clear
  C)
  2hr done clear
  D)
  4hr done clear
  View Solution play_arrow

• question_answer89)
  A satellite can be in a geostationary orbit around earth at a distance r from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the centre is
  A)
  \[\frac{r}{2}\]                done clear
  B)
         \[\frac{r}{2\sqrt{2}}\] done clear
  C)
  \[\frac{r}{{{\left( 4 \right)}^{1/3}}}\]      done clear
  D)
         \[\frac{r}{{{\left( 2 \right)}^{1/3}}}\] done clear
  View Solution play_arrow

• question_answer90)
  The mass M of a planet-earth is uniformly distributed over a spherical volume of radius R. Calculate the energy needed to disassemble the planet against the gravitational pull amongst its constituent particles. Given: \[\operatorname{MR}=2.5\times 1{{0}^{31}} kg-mandg= 10m/{{s}^{2}}\]
  A)
  \[3.0\times {{10}^{32}}\operatorname{J}\]        done clear
  B)
  \[2.5\times {{10}^{32}}\operatorname{J}\] done clear
  C)
  \[0.5\times {{10}^{32}}\operatorname{J}\]     done clear
  D)
         \[1.5\times {{10}^{32}}\operatorname{J}\] done clear
  View Solution play_arrow

• question_answer91)
  Two bodies of masses \[{{M}_{1}}\text{ }\operatorname{and}\text{ }{{M}_{2}}\]are placed at a distanced/apart. What is the potential at the position where the gravitational field due to them is zero?
  A)
  \[-\frac{G}{d}({{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] done clear
  B)
  \[-\frac{G}{d}({{M}_{1}}+{{M}_{2}}-2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] done clear
  C)
  \[-\frac{G}{d}(2{{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] done clear
  D)
  \[-\frac{G}{2d}({{M}_{1}}+{{M}_{2}}+2\sqrt{{{M}_{1}}}\sqrt{{{M}_{2}}})\] done clear
  View Solution play_arrow

• question_answer92)
  At what height from the surface of earth the gravitational potential and the value of g are\[-5.4\times 1{{0}^{7}}J k{{g}^{-1}} and 6.0 m{{s}^{-2}}\]respectively? Take the radius of earth as 6400 km:
  A)
  2600 km            done clear
  B)
  1600 km done clear
  C)
  1400 km         done clear
  D)
         2000 km done clear
  View Solution play_arrow

• question_answer93)
  Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer94)
  The gravitational potential of two homogeneous spherical shells A and B of same surface density at their respective centres are in the ratio 3 : 4. If the two shells coalesce into single one such that surface charge density remains same, then the ratio of potential at an internal point of the view shell to shell A is equal to
  A)
  3:2                    done clear
  B)
         4:3  done clear
  C)
  5:3                    done clear
  D)
         5:6 done clear
  View Solution play_arrow

• question_answer95)
  The gravitational field in a region is given by\[\vec{g} =5N/kg\hat{i}+12N/kg\hat{j}\]. The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point \[(7m,-3m)\] is:
  A)
  \[71\text{ }J\] done clear
  B)
  \[13\sqrt{58}J\] done clear
  C)
  \[-71\text{ }J\] done clear
  D)
  \[1\text{ }J\] done clear
  View Solution play_arrow

• question_answer96)
  The gravitational field due to a mass distribution is \[\operatorname{E}=K/{{x}^{3}}\]in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is
  A)
  \[K/x\] done clear
  B)
  \[K/2x\] done clear
  C)
  \[\operatorname{K}/{{x}^{2}}\] done clear
  D)
  \[\operatorname{K}/2{{x}^{2}}\] done clear
  View Solution play_arrow

• question_answer97)
  Infinite number of masses, each 1 kg are placed along the x-axis \[\operatorname{at} x=\pm  1 m, \pm  2m, \pm  4m, \pm \]\[8m, \pm 16M\ldots \] the magnitude of the resultant gravitational potential in terms of gravitational constant G at the or g in \[(x=0)\] is
  A)
  G/2 done clear
  B)
  G    done clear
  C)
  2G   done clear
  D)
  4G done clear
  View Solution play_arrow

• question_answer98)
  Two rings each of radius 'a' are coaxial and the distance between their centres is a. The masses of the rings are\[{{M}_{1}}\text{ }and\text{ }{{M}_{2}}\]. The work done in transporting a particle of a small mass m from centre \[{{\operatorname{C}}_{1}} to {{C}_{2}}\]is :
  A)
  \[\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{a}\] done clear
  B)
         \[\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{a\sqrt{2}}\left( \sqrt{2}+1 \right)\] done clear
  C)
  \[\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{a\sqrt{2}}\left( \sqrt{2}-1 \right)\] done clear
  D)
  \[\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{\sqrt{2}}a\] done clear
  View Solution play_arrow

• question_answer99)
  A system consists of two stars of equal masses that revolve in a circular orbit about a centre of mass midway between them. Orbital speed of each star is v and period is T. Find the mass M of each star (G is gravitational constant)                     
  A)
  \[\frac{2G{{v}^{3}}}{\pi T}\] done clear
  B)
  \[\frac{{{v}^{3}}T}{\pi G}\] done clear
  C)
  \[\frac{{{v}^{3}}T}{2\pi G}\] done clear
  D)
  \[\frac{2T{{v}^{3}}}{\pi G}\] done clear
  View Solution play_arrow

• question_answer100)
  A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\] as shown in the figure. The gravitational field due to the ring at a distance \[\sqrt{3}r\]is.
  A)
  \[\frac{Gm}{8{{r}^{2}}}\] done clear
  B)
  \[\frac{Gm}{4{{r}^{2}}}\] done clear
  C)
  \[\sqrt{3}\frac{Gm}{8{{r}^{2}}}\] done clear
  D)
  \[\frac{Gm}{8{{r}^{2}}\sqrt{3}}\] done clear
  View Solution play_arrow