Quiz - physics - Gravitation-PYQ

Q1. The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then Source: orcusprep.in

NEET 2018

medium

K_A < K_B < K_C

K_A > K_B > K_C

K_B < K_A < K_C

K_B > K_A > K_C

Q2. A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is Source: orcusprep.in

AIPMT 2011

medium

(r₁/r₂)²

r₂/r₁

(r₂/r₁)²

r₁/r₂

Q3. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B then Source: orcusprep.in

AIPMT 2009

medium

t₁ = 4t₂

t₁ = 2t₂

t₁ = t₂

t₁ > t₂

Q4. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun? Source: orcusprep.in

AIPMT 1997

easy

4

5

2

3

Q5. The distance of two planets from the sun are 10¹³ m and 10¹² m respectively. The ratio of time periods of the planets is Source: orcusprep.in

AIPMT 1994

easy

10

10√10

√10

1/10

Q6. A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct? Source: orcusprep.in

AIPMT 1990

medium

T is conserved

V is always positive

E is always negative

L is conserved but direction of vector L changes continuously

Q7. The largest and the shortest distance of the earth from the sun are r₁ and r₂. Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is Source: orcusprep.in

AIPMT 1988

hard

(r₁ + r₂)/4

r₁r₂/(r₁ + r₂)

2r₁r₂/(r₁ + r₂)

(r₁ + r₂)/3

Q8. Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will Source: orcusprep.in

NEET 2017

easy

move towards each other

move away from each other

will become stationary

keep floating at the same distance between them

Q9. Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T² = Kr³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = GMm/r², here G is gravitational constant. The relation between G and K is described as Source: orcusprep.in

NEET 2015

medium

K = G

K = 1/G

GK = 4π²

GMK = 4π²

Q10. Dependence of intensity of gravitational field ($E$) of earth with distance ($r$) from centre of earth is correctly represented by Source: orcusprep.in

AIPMT 2014

medium

Option A

Option B

Option C

Option D

Q11. 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) Source: orcusprep.in

AIPMT 2012

medium

Option A

Option B

Option C

Option D

Q12. 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 Source: orcusprep.in

AIPMT 2003

easy

$3F$

$F$

$F/3$

$F/9$

Q13. Gravitational force is required for Source: orcusprep.in

AIPMT 2000

easy

stirring of liquid

convection

conduction

radiation

Q14. A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be Source: orcusprep.in

AIPMT 2000

medium

$36 \, \text{N}$

$32 \, \text{N}$

$144 \, \text{N}$

$50 \, \text{N}$

Q15. Two particles of equal mass $m$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed $v$ of each particle is Source: orcusprep.in

AIPMT 1995

medium

$\frac{1}{2}\sqrt{\frac{Gm}{R}}$

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

$\frac{1}{2R}\sqrt{Gm}$

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

Q16. The earth (mass $= 6 \times 10^{24} \, \text{kg}$) revolves around the sun with an angular velocity of $2 \times 10^{-7} \, \text{rad/s}$ in a circular orbit of radius $1.5 \times 10^8 \, \text{km}$. The force exerted by the sun on the earth, in newton, is Source: orcusprep.in

AIPMT 1995

medium

$36 \times 10^{21}$

$27 \times 10^{39}$

zero

$18 \times 10^{25}$

Q17. If the gravitational force between two objects were proportional to $1/R$ (and not as $1/R^2$), where $R$ is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed $v$, proportional to Source: orcusprep.in

AIPMT 1994

hard

$R$

$R^0$ (independent of $R$)

$1/R^2$

$1/R$

Q18. If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? Source: orcusprep.in

NEET 2018

medium

Raindrops will fall faster

Walking on the ground would become more difficult

Time period of a simple pendulum on the Earth would decrease

$g$ on the Earth will not change

Q19. A spherical planet has a mass $M_p$ and diameter $D_p$. A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to Source: orcusprep.in

AIPMT 2012

easy

$\frac{4GM_p}{D_p^2}$

$\frac{GM_p m}{D_p^2}$

$\frac{GM_p}{D_p^2}$

$\frac{4GM_p m}{D_p^2}$

Q20. 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 Source: orcusprep.in

AIPMT 2005

medium

$g' = g/9$

$g' = 27g$

$g' = 9g$

$g' = 3g$

Q21. 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 Source: orcusprep.in

AIPMT 2004

medium

$2R$

$4R$

$\frac{1}{4}R$

$\frac{1}{2}R$

Q22. 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 2 m on the surface of A. What is the height of jump by the same person on the planet B? Source: orcusprep.in

AIPMT 2003

medium

$(2/9) \, \text{m}$

$18 \, \text{m}$

$6 \, \text{m}$

$(2/3) \, \text{m}$

Q23. What will be the formula of mass of the earth in terms of $g$, $R$ and $G$? Source: orcusprep.in

AIPMT 1996

easy

$\frac{GR}{g}$

$\frac{gR^2}{G}$

$\frac{gR}{G}$

$\frac{Gg}{R}$

Q24. The acceleration due to gravity $g$ and mean density of the earth $\rho$ are related by which of the following relations? (where $G$ is the gravitational constant and $R$ is the radius of the earth.) Source: orcusprep.in

AIPMT 1995

medium

$\rho = \frac{3g}{4\pi GR}$

$\rho = \frac{3g}{4\pi GR^3}$

$\rho = \frac{4\pi gR^2}{3G}$

$\rho = \frac{4\pi gR^3}{3G}$

Q25. The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be Source: orcusprep.in

AIPMT 1994

medium

$20 \, \text{N}$

$8 \, \text{N}$

$80 \, \text{N}$

$40 \, \text{N}$

Q26. A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth? Source: orcusprep.in

NEET 2020

medium

$48 \, \text{N}$

$32 \, \text{N}$

$30 \, \text{N}$

$24 \, \text{N}$

Q27. A body weighs 200 N on the surface of the earth. How much will it weigh half way down to the centre of the earth? Source: orcusprep.in

NEET 2019

medium

$100 \, \text{N}$

$150 \, \text{N}$

$200 \, \text{N}$

$250 \, \text{N}$

Q28. The acceleration due to gravity at a height 1 km above the earth is the same as at a depth $d$ below the surface of earth. Then Source: orcusprep.in

NEET 2017

medium

$d = 1 \, \text{km}$

$d = \frac{3}{2} \, \text{km}$

$d = 2 \, \text{km}$

$d = \frac{1}{2} \, \text{km}$

Q29. Starting from the centre of the earth having radius $R$, the variation of $g$ (acceleration due to gravity) is shown by Source: orcusprep.in

NEET 2016

medium

Option A

Option B

Option C

Option D

Q30. The height at which the weight of a body becomes $\frac{1}{16}$th, its weight on the surface of earth (radius $R$), is Source: orcusprep.in

AIPMT 2012

medium

$5R$

$15R$

$3R$

$4R$

Q31. The work done to raise a mass $m$ from the surface of the earth to a height $h$, which is equal to the radius of the earth, is Source: orcusprep.in

NEET 2019

medium

$\frac{3}{2}mgR$

$mgR$

$2mgR$

$\frac{1}{2}mgR$

Q32. At what height from the surface of earth the gravitation potential and the value of $g$ are $-5.4 \times 10^7 \, \text{J kg}^{-1}$ and $6.0 \, \text{m s}^{-2}$ respectively? Take the radius of earth as 6400 km. Source: orcusprep.in

NEET 2016

hard

$1400 \, \text{km}$

$2000 \, \text{km}$

$2600 \, \text{km}$

$1600 \, \text{km}$

Q33. Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m, ..., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be Source: orcusprep.in

NEET 2013

hard

$-\frac{4}{3}G$

$-4G$

$-G$

$-\frac{8}{3}G$

Q34. A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius ($R$) of the earth. The change in potential energy of body will be Source: orcusprep.in

NEET 2013

medium

$3mgR$

$\frac{1}{3}mgR$

$mg \cdot 2R$

$\frac{2}{3}mgR$

Q35. A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre, will be Source: orcusprep.in

AIPMT 2011

hard

$\frac{GM}{a}$

$\frac{2GM}{a}$

$\frac{3GM}{a}$

$\frac{4GM}{a}$

Q36. The ratio of escape velocity at earth ($v_e$) to the escape velocity at a planet ($v_p$) whose radius and mean density are twice as that of earth is Source: orcusprep.in

NEET 2016

medium

$1 : 4$

$1 : \sqrt{2}$

$1 : 2$

$1 : 2\sqrt{2}$

Q37. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = $5.98 \times 10^{24}$ kg) have to be compressed to be a black hole? Source: orcusprep.in

NEET 2014

medium

$10^{-9} \, \text{m}$

$10^{-6} \, \text{m}$

$10^{-2} \, \text{m}$

$100 \, \text{m}$

Q38. The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. $V_P$ and $V_E$ are escape velocities of the planet and the earth, respectively, then Source: orcusprep.in

NEET 2013

medium

$V_P = 1.5 V_E$

$V_P = 2 V_E$

$V_E = 3 V_P$

$V_E = 1.5 V_P$

Q39. A particle of mass $m$ is kept at rest at a height $3R$ from the surface of earth, where $R$ is radius of earth and $M$ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is ($g$ is acceleration due to gravity on the surface of earth) Source: orcusprep.in

NEET 2013

hard

$\left(\frac{GM}{2R}\right)^{1/2}$

$\left(\frac{gR}{4}\right)^{1/2}$

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

$\left(\frac{GM}{R}\right)^{1/2}$

Q40. The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the earth. The escape velocity of a body from this platform is $fv$, where $v$ is its escape velocity from the surface of the Earth. The value of $f$ is Source: orcusprep.in

AIPMT 2006

medium

$1/2$

$\sqrt{2}$

$1/\sqrt{2}$

$1/3$

Q41. For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. The escape velocity for this planet will be Source: orcusprep.in

AIPMT 2000

medium

$11.2 \, \text{km/s}$

$22.4 \, \text{km/s}$

$5.6 \, \text{km/s}$

$44.8 \, \text{km/s}$

Q42. The escape velocity of a sphere of mass $m$ is given by ($G$ = Universal gravitational constant; $M_e$ = Mass of the earth and $R_e$ = Radius of the earth) Source: orcusprep.in

AIPMT 1999

easy

$\sqrt{\frac{2GM_e m}{R_e}}$

$\sqrt{\frac{2GM_e}{R_e}}$

$\sqrt{\frac{GM_e}{R_e}}$

$\sqrt{\frac{2GM_e R_e}{R_e}}$

Q43. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes Source: orcusprep.in

AIPMT 1997

medium

$22.4 \, \text{km/s}$

$44.8 \, \text{km/s}$

$5.6 \, \text{km/s}$

$11.2 \, \text{km/s}$

Q44. The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is Source: orcusprep.in

AIPMT 1993

easy

$11.2 \times 2 \, \text{km/s}$

$11.2 \, \text{km/s}$

$11.2/\sqrt{2} \, \text{km/s}$

$11.2\sqrt{2} \, \text{km/s}$

Q45. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of $60^\circ$ with the vertical, then escape velocity will be Source: orcusprep.in

AIPMT 1989

easy

$11 \, \text{km/s}$

$11\sqrt{3} \, \text{km/s}$

$\frac{11}{\sqrt{3}} \, \text{km/s}$

$33 \, \text{km/s}$

Q46. The time period of a geostationary satellite is 24 h, at a height $6R_E$ ($R_E$ is radius of earth) from surface of earth. The time period of another satellite whose height is $2.5R_E$ from surface will be Source: orcusprep.in

NEET 2019

medium

$6\sqrt{2} \, \text{h}$

$12\sqrt{2} \, \text{h}$

$\frac{24}{2.5} \, \text{h}$

$\frac{12}{2.5} \, \text{h}$

Q47. A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25 \times 10^6 \, \text{m}$ above the surface of earth. If earth's radius is $6.38 \times 10^6 \, \text{m}$ and $g = 9.8 \, \text{m/s}^2$, then the orbital speed of the satellite is Source: orcusprep.in

AIPMT 2015

medium

$9.13 \, \text{km/s}$

$6.67 \, \text{km/s}$

$7.76 \, \text{km/s}$

$8.56 \, \text{km/s}$

Q48. 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. Then Source: orcusprep.in

AIPMT 2015

medium

the linear momentum of S remains constant in magnitude

the acceleration of S is always directed towards the centre of the earth

the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

the total mechanical energy of S varies periodically with time

Q49. A geostationary satellite is orbiting the earth at a height of $5R$ above the surface of the earth, $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is Source: orcusprep.in

AIPMT 2012

medium

$5$

$10$

$6\sqrt{2}$

$\frac{6}{\sqrt{2}}$

Q50. If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by Source: orcusprep.in

AIPMT 2012

easy

$v_o = \sqrt{2}v_e$

$v_o = v_e$

$v_e = \sqrt{2}v_o$

$v_e = 2v_o$

Q51. The radii of circular orbits of two satellites A and B of the earth, are $4R$ and $R$, respectively. If the speed of satellite A is $3V$, then the speed of satellite B will be Source: orcusprep.in

AIPMT 2010

medium

$\frac{3}{4}V$

$6V$

$12V$

$\frac{3}{2}V$

Q52. A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball? Source: orcusprep.in

AIPMT 1996

medium

it will fall down to the earth gradually

it will go very far in the space

it will continue to move with the same speed along the original orbit of spacecraft

it will move with the same speed, tangentially to the spacecraft

Q53. A satellite A of mass $m$ is at a distance of $r$ from the centre 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 Source: orcusprep.in

AIPMT 1993

medium

$1 : 2$

$1 : 16$

$1 : 32$

$1 : 2\sqrt{2}$

Q54. A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth's surface, is Source: orcusprep.in

NEET 2016

medium

$\frac{mg_0 R^2}{2(R + h)}$

$-\frac{mg_0 R^2}{2(R + h)}$

$\frac{2mg_0 R^2}{R + h}$

$-\frac{2mg_0 R^2}{R + h}$

Q55. The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2$ ($R_2 > R_1$) is Source: orcusprep.in

AIPMT 2010

hard

$GmM\left(\frac{1}{R_1^2} - \frac{1}{R_2^2}\right)$

$GmM\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$

$2GmM\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$

$\frac{1}{2}GmM\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$

Q56. Two satellites of earth, $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statements is true? Source: orcusprep.in

AIPMT 2007

medium

The potential energies of earth and satellite in the two cases are equal

$S_1$ and $S_2$ are moving with the same speed

The kinetic energies of the two satellites are equal

The time period of $S_1$ is four times that of $S_2$

Q57. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is Source: orcusprep.in

AIPMT 2005

easy

$1/2$

$1/\sqrt{2}$

$\sqrt{2}$

$2$

Q58. The satellite of mass $m$ is orbiting around the earth in a circular orbit with a velocity $v$. What will be its total energy? Source: orcusprep.in

AIPMT 1991

medium

$(3/4)mv^2$

$(1/2)mv^2$

$mv^2$

$-(1/2)mv^2$

Q59. The mean radius of earth is $R$, its angular speed on its own axis is $\omega$ and the acceleration due to gravity at earth's surface is $g$. What will be the radius of the orbit of a geostationary satellite? Source: orcusprep.in

AIPMT 1992

hard

$(R^2g/\omega^2)^{1/3}$

$(Rg/\omega^2)^{1/3}$

$(R^2\omega^2/g)^{1/3}$

$(R^2g/\omega)^{1/3}$

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Physics - Gravitation-PYQ

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Physics - Gravitation-PYQ

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