Solved papers for JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण JEE PYQ-Gravitation

done JEE PYQ-Gravitation Total Questions - 73

• question_answer1) If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will                                                                                            [AIEEE 2002]

A)
continue to move in its orbit with same velocity

B)
move tangentially to the original orbit with the same velocity

C)
become stationary in its orbit

D)
move towards the earth

• question_answer2) Energy required to move a body of mass m from an orbit of radius 2 R to 3 R is                      [AIEEE 2002]

A)
$GMm/12{{R}^{2}}$

B)
$GMm/3{{R}^{2}}$

C)
$GMm/8R$

D)
$GMm/6R$

• question_answer3) The escape velocity of a body depends upon mass as                                                                       [AIEEE 2002]

A)
${{m}^{o}}$

B)
${{m}^{1}}$

C)
${{m}^{2}}$

D)
${{m}^{3}}$

• question_answer4) The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is     [AIEEE 2002]

A)
$\frac{mgR}{2}$

B)
2mgR

C)
mgR

D)
$\frac{mgR}{4}$

• question_answer5) The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become                                                                              [AIEEE 2003]

A)
10 h

B)
80 h

C)
40 h

D)
20 h

• question_answer6) Two spherical bodies of mass M and 5 M and radii R and 2 R 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                                                                                   [AIEEE 2003]

A)
$2.5$ R

B)
$4.5$ R

C)
$7.5$ R

D)
$1.5$ R

• question_answer7) The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of ${{45}^{o}}$ with the vertical, the escape velocity will be                                    [AIEEE 2003]

A)
$11\sqrt{2}$ km/s

B)
22 km/s

C)
11 km/s

D)
$11\sqrt{2}$ m/s

• question_answer8)   A satellite of mass$m$revolve around the earth of radius R at a bright$x$from its surface. If$g$is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellites is          [AIEEE 2004]

A)
$gx$

B)
$\frac{gR}{R-x}$

C)
$\frac{g{{R}^{2}}}{R+x}$

D)
${{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}$

• question_answer9) The time period of an earth satellite in circular orbit is independent of                [AIEEE 2004]

A)
the mass of the satellite

B)

C)
both the mass and radius of the orbit

D)
neither the mass of the satellite nor the radius of its orbit

• question_answer10) 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                            [AIEEE 2004]

A)
$2\text{ }mgR$

B)
$\frac{1}{2}mgR$

C)
$\frac{1}{4}mgR$

D)
$mgR$

• question_answer11) Suppose the gravitational force varies inversely as the nth 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)
${{R}^{\left( \frac{n+1}{2} \right)}}$

B)
${{R}^{\left( \frac{n-1}{2} \right)}}$

C)
${{R}^{n}}$

D)
${{R}^{\left( \frac{n-2}{2} \right)}}$

• question_answer12) The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is to in air. Neglecting frictional force of water and given that the density of the bob is$(4/3)\times 1000$$kg/{{m}^{3}}$. What relationship between t and${{t}_{0}}$is true?                                      [AIEEE 2004]

A)
$t={{t}_{0}}$

B)
$t={{t}_{0}}/2$

C)
$t=2{{t}_{0}}$

D)
$t=4{{t}_{0}}$

• question_answer13) Average density of the earth                                                                                  [AIEEE 2005]

A)
does not depend on g

B)
is a complex function of g

C)
is directly proportional to g

D)
is inversely proportional to g

• question_answer14) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?                                                                                                                                                           [AIEEE 2005]

A)
$d=\frac{h}{2}$

B)
$d=\frac{3h}{2}$

C)
$d=2h$

D)
$d=h$

• question_answer15) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere. (You may take $G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}$)                                            [AIEEE 2005]

A)
$13.34\times {{10}^{-10}}J$

B)
$3.33\times {{10}^{-10}}J$

C)
$6.67\times {{10}^{-9}}J$

D)
$6.67\times {{10}^{-10}}J$

• question_answer16) If$\frac{1}{6}$arid$\frac{1}{3}$are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio $\frac{\text{electronic charge on the moon}}{\text{electronic charge on the earth}}$ to be                       [AIEEE 2007]

A)
1

B)
zero

C)
$\sqrt{5},$

D)
$(-3,\infty )$

• question_answer17) This question contains Statement-1 and Statement -2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: For a mass M kept at the canter of a cube of side a the flux of gravitational field passing through its sides is $4\pi$ GM. Statement -2: If the direction of a field due to a point source is radial and its dependence on the distance r from the source is given as$\frac{1}{{{r}^{2}}}$, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.                                                              [AIEEE 2008]

A)
Statement -1 is true, Statement- 2 is true; Statement -2 is not a correct explanation for Statement-1

B)
Statement-1 is true, Statement- 2 is false

C)
Statement-1 is false, Statement- 2 is true

D)
Statement-1 is true, Statement- 2 is true; Statement-2 is a correct explanation for Statement-1

• question_answer18) A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 $km\,{{s}^{-1}}$, the escape velocity from the surface of the planet would be: [AIEEE 2008]

A)
110 $km\,{{s}^{-1}}$

B)
0.11 $km\,{{s}^{-1}}$

C)
1.1 $km\,{{s}^{-1}}$

D)
11 $km\,{{s}^{-1}}$

• question_answer19) The height at which the acceleration due to gravity becomes$\frac{g}{9}$(where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is:                                                [AIEEE 2009]

A)
2R

B)
$\frac{R}{\sqrt{2}}$

C)
R/2

D)
$\sqrt{2}R$

• question_answer20) Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is                                                                             [AIEEE 2011]

A)
$-\frac{9Gm}{r}$

B)
Zero

C)
$-\frac{4Gm}{r}$

D)
$-\frac{6Gm}{r}$

• question_answer21) 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 partial with respect to their centre of mass is:           [AIEEE 11-05-2011]

A)
$\sqrt{\frac{Gm}{4R}}$

B)
$\sqrt{\frac{Gm}{3R}}$

C)
$\sqrt{\frac{Gm}{2R}}$

D)
$\sqrt{\frac{Gm}{R}}$

• question_answer22) The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are $10\,m/{{s}^{2}}$ and 6400 km respectively. The required energy for this work will be:                                                                                                                                       [AIEEE 2012]

A)
$6.4\times {{10}^{11}}$ Joules

B)
$6.4\times {{10}^{8}}$ Joules

C)
$6.4\times {{10}^{9}}$ Joules

D)
$6.4\times {{10}^{10}}$ Joules

• question_answer23) Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth$={{R}_{E}}$)?                                                                    [JEE ONLINE 07-05-2012]

A)

B)

C)

D)

• question_answer24) Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to                                                               [JEE ONLINE 12-05-2012]

A)
r

B)
${{r}^{-1}}$

C)
${{r}^{2}}$

D)
${{r}^{-2}}$

• question_answer25) Two point masses of mass ${{m}_{1}}=fM$and ${{m}_{2}}=(1-f)M(f<1)$are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ${{\omega }_{1}}$) for${{m}_{1}}$and ${{\omega }_{2}}$for${{m}_{2}}$. In that case                                                                                                          [JEE ONLINE 19-05-2012]

A)
$(1-f){{\omega }_{1}}=f\omega$

B)
${{\omega }_{1}}={{\omega }_{2}}$and independent of f

C)
$f{{\omega }_{1}}=(1-f){{\omega }_{2}}$

D)
${{\omega }_{1}}={{\omega }_{2}}$ and depend on f

• question_answer26)   A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be         [JEE ONLINE 26-05-2012]

A)
$\sqrt{\frac{2Gm}{r}\left( \sqrt{2}-1 \right)}$

B)
$\sqrt{\frac{Gm}{r}}$

C)
$\sqrt{\frac{2Gm}{r}\left( 1-\frac{1}{\sqrt{2}} \right)}$

D)
$\sqrt{\frac{2Gm}{r}}$

• question_answer27) What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?                                                                           [JEE MAIN 2013]

A)
$\frac{5GmM}{6R}$

B)
$\frac{2GmM}{3R}$

C)
$\frac{GmM}{2R}$

D)
$\frac{GmM}{3R}$

• question_answer28)  The gravitational filed, 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)   [JEE ONLINE 09-04-2013]

A)
$\frac{5}{6}\frac{GM}{{{x}^{2}}}$

B)
$\frac{8}{9}\frac{GM}{{{x}^{2}}}$

C)
$\frac{7}{8}\frac{GM}{{{x}^{2}}}$

D)
$\frac{6}{7}\frac{GM}{{{x}^{2}}}$

• question_answer29) 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 $=7.36\times {{10}^{22}}\,kg$, radius of the moons orbit $=3.8\times {{10}^{8}}\,m$)   [JEE ONLINE 22-04-2013]

A)
$6.73\times {{10}^{-5}}\operatorname{m}/{{\operatorname{s}}^{2}}$

B)
$6.73\times {{10}^{-.6}}\operatorname{m}/{{\operatorname{s}}^{2}}$

C)
$6.73\times {{10}^{-.2}}\operatorname{m}/{{\operatorname{s}}^{2}}$

D)
$6.73\times {{10}^{-.4}}\operatorname{m}/{{\operatorname{s}}^{2}}$

• question_answer30) The gravitational field in a region is given by: $\vec{E}=(5N/kg)\,\hat{i}+(12\,N/kg)\,\hat{j}$ If the potential at the origin is taken to be zero, then the ratio of the potential at the points (12m, 0) and (0, 5m) is:                                                                                                    [JEE ONLINE 25-04-2013]

A)
Zero

B)
1  $6.73\times {{10}^{-.3}}\operatorname{m}/{{\operatorname{s}}^{2}}$

C)
$\frac{144}{25}$

D)
$\frac{25}{144}$

• question_answer31) Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:                                              [JEE MAIN 2014]

A)
$\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}$

B)
$\frac{1}{2}\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}$

C)
$\sqrt{\frac{GM}{R}}$

D)
$\sqrt{2\sqrt{2}\frac{GM}{R}}$

• question_answer32)  Indias Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earths orbit is ${{a}_{e}}=1.5\times {{10}^{11}}m,$ that of Mars orbit ${{a}_{m}}=2.28\times {{10}^{11}}m,$m, taken Keplers laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to:                                                                                            [JEE ONLINE 09-04-2014] 4)

A)
500 days

B)
320 days

C)
260 days

D)
220 days

• question_answer33)  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: [JEE ONLINE 11-04-2014]

A)
$\frac{41G{{M}^{2}}}{3600{{R}^{2}}}$

B)
$\frac{41G{{M}^{2}}}{450{{R}^{2}}}$

C)
$\frac{59\,G{{M}^{2}}}{450{{R}^{2}}}$

D)
$\frac{\,G{{M}^{2}}}{225{{R}^{2}}}$

• question_answer34)  Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is d? (Speed of ${{m}_{1}}$ is ${{v}_{1}}$ and that of ${{m}_{2}}$ is ${{v}_{2}}$)          [JEE ONLINE 12-04-2014]

A)
${{v}_{1}}={{v}_{2}}$

B)
${{v}_{1}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}$ ${{v}_{2}}={{m}_{1}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}$

C)
${{v}_{1}}={{m}_{1}}\sqrt{\frac{2G}{d\left({{m}_{1}}+{{m}_{2}}\right)}}$${{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}$

D)
${{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{1}}}}$            ${{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{2}}}}$

• question_answer35) Match List - I (Event) with List-II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists                                               [JEE ONLINE 19-04-2014]  List I List-II (1) Rotation period of earth (i) ${{10}^{5}}s$ (2) Revolution period of earth (ii) ${{10}^{7}}s$ (3) Period of light wave (iii) ${{10}^{-15}}s$ (4) Period of sound wave (iv) ${{10}^{-3}}s$

A)
(1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)

B)
(1)-(ii), (2)-(i), (3)-(iv), (4)-(iii)

C)
(1)-(i), (2)-(ii), (3)-(iv), (4)-(iii)

D)
(1)-(ii), (2)-(i), (3)-(iii), (4)-(iv)

• question_answer36) The gravitational field in a region is given by $\overset{\to }{\mathop{g}}\,=5N/kg\hat{i}+12N/kg\hat{j}.$The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7 m,  3 m) is:      [JEE ONLINE 19-04-2014]

A)
71 J

B)
13 58 J

C)
71 J

D)
1 J

• question_answer37)  In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of g at the place?                                                           [JEE ONLINE 19-04-2014]

A)
$9.81m/{{s}^{2}}$

B)
$9.87m/{{s}^{2}}$

C)
$9.91m/{{s}^{2}}$

D)
$10.0m/{{s}^{2}}$

• question_answer38)  From a solid sphere of mass M and radius R, a spherical portion of radius $\frac{R}{2}$is removed, as shown in the figure. Taking gravitational potential V = 0 at $r=\infty ,$ the potential at the centre of cavity thus formed is: (G = gravitational constant)                                                                                             [JEE MAIN 2015]

A)
$\frac{-2GM}{3R}$

B)
$\frac{-2GM}{R}$

C)
$\frac{-GM}{2R}$

D)
$\frac{-GM}{R}$

• question_answer39) A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxys axis is r, then:                                        [JEE ONLINE 10-04-2015]

A)
$T\propto {{r}^{2}}$

B)
$T\propto r$

C)
${{T}^{2}}\propto {{r}^{3}}$

D)
$T\propto \sqrt{r}$

• question_answer40) Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density? (figures are not drawn to scale)                            [JEE MAIN 11-04-2015]

A)

B)

C)

D)

• question_answer41) A satellite is reolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R ; h << R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to:                                                                                                                                                [JEE MAIN - I 3-4-2016] (Neglect the effect of atmosphere).

A)
$\sqrt{gR}\left( \sqrt{2}-1 \right)$

B)
$\sqrt{2gR}$

C)
$\sqrt{gR}$

D)
$\sqrt{gR/2}$

• question_answer42) Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle $csa$is$\frac{1}{4}$the area of the ellipse. (See figure) With db as the semi major axis, and ca as the semi minor axis. If ${{t}_{1}}$is the time taken for planet to go over path $abc$ and ${{t}_{2}}$for path taken over $cda$ then:          [JEE ONLINE 09-04-2016]

A)
${{t}_{1}}=3{{t}_{2}}$

B)
${{t}_{1}}={{t}_{2}}$

C)
${{t}_{1}}=2{{t}_{2}}$

D)
${{t}_{1}}=4{{t}_{2}}$

• question_answer43) An astronaut of mass m is working on a satellite orbiting the earth at a distance h. from the earth's surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is:               [JEE ONLINE 10-04-2016]

A)
${{F}_{G}}\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}$

B)
zero since astronaut feels weightless

C)
$\frac{G{{M}_{m}}}{{{\left( R+h \right)}^{2}}}<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}$

D)
$0<{{F}_{G}}<\frac{G{{M}_{m}}}{{{R}^{2}}}$

• question_answer44) The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius):                                                                                                                                    [JEE Main 2017]

A)

B)

C)

D)

• question_answer45) If the earth has no rotational motion, the weight of a person on the equation is W. Detrmine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight$\frac{3}{4}W.$Radius of the earth is 6400 km and $g=10m/{{s}^{2}}.$                                                                           [JEE Online 08-04-2017]

A)
$0.63\times {{10}^{-3}}rad/s$

B)
$0.28\times {{10}^{-3}}rad/s$

C)
$1.1\times {{10}^{-3}}rad/s$

D)
$0.83\times {{10}^{-3}}rad/s$

• question_answer46) The mass density of a spherical body is given by $\rho (r)\,=\frac{k}{r}$ for $r\le R$ and $\rho \,(r)=0$ for $r>R,$ Where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is -                                                                                      [JEE Online 09-04-2017]

A)

B)

C)

D)

• question_answer47) A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the ${{\text{n}}^{\text{th}}}$ power of R. If the period of rotation of the particle is T, then: [JEE Main Online 08-04-2018]

A)
$\text{T}\propto {{\text{R}}^{(n+1)/2}}$

B)
$\text{T}\propto {{\text{R}}^{n/2}}$

C)
$\text{T}\propto {{\text{R}}^{3/2}}$ for any $n$

D)
$T\propto {{R}^{\frac{n}{2}+1}}$

• question_answer48) A body of mass $m$ is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$, and the other mass, in a circular orbit of radius $\frac{3R}{2}$. The difference between the final initial total energies is:        [JEE Online 15-04-2018]

A)
$-\frac{GMm}{2R}$

B)
$+\frac{GMm}{6R}$

C)
$-\frac{GMm}{6R}$

D)
$\frac{GMm}{2R}$

• question_answer49) Take the mean distance of the moon and the sun from the earth to be $0.4\times {{10}^{6}}km$and $150\times {{10}^{6}}km$ respectively. Their masses are $8\times {{10}^{22}}kg$and $2\times {{10}^{30}}kg$ respectively. The radius of the earth is$6400km$. Let $\Delta {{F}_{1}}$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $\Delta {{F}_{2}}$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $\frac{\Delta {{F}_{1}}}{\Delta {{F}_{2}}}$ is: [JEE Online 15-04-2018]

A)
2

B)
6

C)
${{10}^{-2}}$

D)
0.6

• question_answer50) The relative uncertainty in the period of a satellite orbiting around the earth is ${{10}^{-2}}.$ If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is      [JEE Main Online 16-4-2018]

A)
$3\times {{10}^{-2}}$

B)
${{10}^{-2}}$

C)
$2\times {{10}^{-2}}$

D)
$6\times {{10}^{-2}}$

• question_answer51)     Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.

A)
There will be no change in weight anywhere on the earth

B)
Weight of the object, everywhere on the earth, will decrease

C)
Weight of the object, everywhere on the earth, will increase

D)
Except at poles, weight of the object on the earth will decrease

• question_answer52) The energy required to take a satellite to a height h above Earth surface (radius of Earth $=6.4\times {{10}^{3}}km$) is ${{E}_{1}}$ and kinetic energy required for the satellite to be in a circular orbit at this height is ${{E}_{2}}$. The value of h for which ${{E}_{1}}$ and ${{E}_{2}}$ are equal, is:                            [JEE Main 09-Jan-2019 Evening]

A)
$3.2\times {{10}^{3}}\text{ }km$

B)
$1.6\times {{10}^{3}}km$

C)
$1.28\times {{10}^{4}}km$

D)
$6.4\times {{10}^{3}}km$

• question_answer53) A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -                                                                                            [JEE Main 10-Jan-2019 Morning]

A)
$m{{v}^{2}}$

B)
$\frac{1}{2}m{{v}^{2}}$

C)
$\frac{3}{2}m{{v}^{2}}$

D)
$2\,m{{v}^{2}}$

• question_answer54) Two stars of masses $3\times {{10}^{31}}$ kg each, and at distance $2\times {{10}^{11}}$ m rotate in a plane about their common centre of mass 0. A meteorite passes through 0 moving perpendicular to the stars rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at 0 is-  (Take       Gravitational      constant;           $G=6.67\times {{10}^{-11}}\,N{{m}^{2}}k{{g}^{-}}^{2})$            [JEE Main 10-Jan-2019 Evening]

A)
$2.4\times {{10}^{4}}m/s$

B)
$1.4\times {{10}^{5}}m/s$

C)
$3.8\times {{10}^{4}}m/s$

D)
$2.8\times {{10}^{5}}m/s$

• question_answer55) A satellite is revolving in a circular orbit at a height h from the earth surface, such that $h<<R$ where R is the radius of the earth.                                        Assuming that the effect of earths atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is-                         [JEE Main 11-Jan-2019 Morning]

A)
$\sqrt{2gR}$

B)
$\sqrt{gR}(\sqrt{2}-1)$

C)
$\sqrt{\frac{gR}{2}}$

D)
$\sqrt{gR}$

• question_answer56) A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely in elastically. The speeds of the satellite and meteorite are the same, just before the collision. The subsequent motion of the combined body will be- [JEE Main 12-Jan-2019 Morning]

A)
in an elliptical orbit

B)
in the same circular orbit of radius R

C)
in a circular orbit of a different radius

D)
such that it escapes to infinity.

• question_answer57)  In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that the variation $\frac{dR}{dl}$of its resistance R with length l is $\frac{dR}{dl}\propto \frac{1}{\sqrt{l}}.$ Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?                                                                                                [JEE Main 12-Jan-2019 Morning]

A)
0.35 m

B)
0.2 m

C)
0.25 m

D)
0.3 m

• question_answer58) A straight rod of length L extends from x=a to $x=L+a.$ The gravitational force it exerts on a point mass m at x=0, if the mass per unit length of the rod is $A+B{{x}^{2}},$, is given by-               [JEE Main 12-Jan-2019 Morning]

A)
$Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)-BL \right]$

B)
$Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)-BL \right]$

C)
$Gm\left[ A\left( \frac{1}{a+L}-\frac{1}{a} \right)+BL \right]$

D)
$Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]$

• question_answer59) Two satellites, A and B, have masses m and 2 m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, $\frac{{{T}_{A}}}{{{T}_{B}}},$is-          [JEE Main 12-Jan-2019 Evening]

A)
1

B)
2

C)
$\sqrt{\frac{1}{2}}$

D)
$\frac{1}{2}$

• question_answer60)  Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square? [JEE Main 8-4-2019 Morning]

A)
$1.21\sqrt{\frac{GM}{a}}$

B)
$1.41\sqrt{\frac{GM}{a}}$

C)
$1.16\sqrt{\frac{GM}{a}}$

D)
$1.35\sqrt{\frac{GM}{a}}$

• question_answer61) A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho (r)=\frac{K}{{{r}^{2}}}.$Identify the correct relation between the radius R of the particle's orbit and its period T :                                                                                                                   [JEE Main 9-4-2019 Afternoon]

A)
$T/{{R}^{2}}$ is a constant

B)
$TR$ is a constant

C)
${{T}^{2}}/{{R}^{3}}$ is a constant

D)
$T/R$ is a constant

• question_answer62) A ball is thrown upward with an initial velocity ${{V}_{0}}$from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma {{\upsilon }^{2}}$ (where m is mass of the ball, $\upsilon$is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is : [JEE Main 10-4-2019 Morning]

A)
$\frac{1}{\sqrt{\gamma g}}{{\sin }^{-1}}\left( \sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$

B)
$\frac{1}{\sqrt{\gamma g}}{{\tan }^{-1}}\left( \sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$  C) $\frac{1}{\sqrt{2\gamma g}}{{\tan }^{-1}}\left( \sqrt{\frac{2\gamma }{g}}{{V}_{0}} \right)$

D)
$\frac{1}{\sqrt{\gamma g}}\ln \left( 1+\sqrt{\frac{\gamma }{g}}{{V}_{0}} \right)$

• question_answer63) Two coaxial discs, having moments of inertia ${{I}_{1}}$and $\frac{{{I}_{1}}}{2},$are rotating with respective angular velocities ${{\omega }_{1}}$and $\frac{{{\omega }_{1}}}{2},$about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If ${{E}_{f}}$and${{E}_{i}}$are the final and initial total energies, then $({{E}_{f}}-{{E}_{i}})$is :                                                                                                                                                [JEE Main 10-4-2019 Morning]

A)
$\frac{{{I}_{1}}\omega _{1}^{2}}{12}$

B)
$\frac{3}{8}{{I}_{1}}\omega _{1}^{2}$

C)
$\frac{{{I}_{1}}\omega _{1}^{2}}{6}$

D)
$\frac{{{I}_{1}}\omega _{1}^{2}}{24}$

• question_answer64) A particle of mass m is moving along a trajectory given by $x={{x}_{0}}+a\cos {{\omega }_{1}}t$ $y={{y}_{0}}+b\sin {{\omega }_{2}}t$ The torque, acting on the particle about the origin, at t = 0 is :                     [JEE Main 10-4-2019 Morning]

A)
$m(-{{x}_{0}}b+{{y}_{0}}a)\omega _{1}^{2}\hat{k}$

B)
$+m{{y}_{0}}a\omega _{1}^{2}\hat{k}$

C)
$-m({{x}_{0}}b\omega _{2}^{2}-{{y}_{0}}a\omega _{1}^{2})\hat{k}$

D)
Zero

• question_answer65) The value of acceleration due to gravity at Earth's surface is . The altitude above its surface at which the acceleration due to gravity decreases to , is close to :(Radius of earth )                                                                                                                                           [JEE Main 10-4-2019 Morning]

A)

B)

C)

D)

• question_answer66)  A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given : Mass of planet Radius of planet Gravitational constant ]                                                                      [JEE Main 10-4-2019 Afternoon]

A)
9

B)
11

C)
13

D)
17

• question_answer67) The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9 : 4. The mass of the planet is th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)                                                                                                        [JEE Main 12-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer68) A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R(R = radius of the earth), it ejects a rocket of mass  so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth): [JEE MAIN Held on 07-01-2020 Morning]

A)
x$5m\left( {{u}^{2}}-\frac{119}{200}\frac{GM}{R} \right)$

B)
$\frac{3m}{8}{{\left( u+\sqrt{\frac{5GM}{6R}} \right)}^{2}}$

C)
$\frac{m}{20}{{\left( u-\sqrt{\frac{2GM}{3R}} \right)}^{2}}$

D)
$\frac{m}{20}\left( {{u}^{2}}+\frac{113}{200}\frac{GM}{R} \right)$

• question_answer69) A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $g=10\text{ }m{{s}^{2}}$at the north pole and the radius of the earth = 6400 km)  [JEE MAIN Held on 07-01-2020 Evening]

A)
194.66 N

B)
195.66 N

C)
195.32 N

D)
194.32 N

• question_answer70)  Consider two solid spheres of radii x${{R}_{1}}=1\text{ }m,$ ${{R}_{2}}=2\text{ }m$ and masses ${{M}_{1}}$and ${{M}_{2}},$respectively. The gravitational field due to sphere  and  are shown. The value of$\frac{{{M}_{1}}}{{{M}_{2}}}$ is [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{1}{6}$

B)
$\frac{1}{2}$

C)
$\frac{2}{3}$

D)
$\frac{1}{3}$

• question_answer71) An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometer/s _____.                                                  [JEE MAIN Held on 08-01-2020 Evening]

• question_answer72) A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass $\frac{m}{2}$ collides with A with a velocity which is half $\left( \frac{{\vec{v}}}{2} \right)$ the instantaneous velocity $\vec{v}$of A. The collision is completely inelastic. Then the combined body                                                                             [JEE MAIN Held on 09-01-2020 Morning]

A)
Escapes from the Planets Gravitational field

B)
Continues to move in a circular orbit

C)
Falls vertically downwards towards the planet

D)
Starts moving in an elliptical orbit around the planet

• question_answer73) Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are ${{\text{v}}_{A}}$and${{\text{v}}_{B}}$, respectively, then$\frac{{{\text{v}}_{A}}}{{{\text{v}}_{B}}}=\frac{n}{4}$. [JEE MAIN Held on 09-01-2020 Evening]

A)
1

B)
4

C)
3

D)
2