Gravitation

200 questions · Physics · JEE Main

Gravitation

200 questions · Physics · JEE Main

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is $\times 1 0^{10} J$ . (Mass of…2025 · 2 Apr · Shift 2 · Q75 · Numerical
$Match the LIST-I with LIST-II$ Choose the correct answer from the options given below: Includes table2025 · 3 Apr · Shift 1 · Q56 · MCQ
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$ . When released, they interact only through gravitational force and collide after a time $T = 4$ seconds. If the sides of the…2025 · 3 Apr · Shift 1 · Q74 · Numerical
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $R$ Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} mgR$ …2025 · 4 Apr · Shift 1 · Q65 · MCQ
An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume $M =$ mass of earth, $G =$ …2025 · 4 Apr · Shift 2 · Q59 · MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity…2025 · 7 Apr · Shift 2 · Q58 · MCQ
A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O$ ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $F_{1}$ . A spherical part of radius $R /3$ … Includes diagram2025 · 22 Jan · Shift 1 · Q50 · MCQ
If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $= 27$ days and gravitational attraction between the satellite and…2025 · 23 Jan · Shift 2 · Q53 · MCQ
A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \frac{GMR}{x}$ . The value of $x$ is …2025 · 23 Jan · Shift 2 · Q75 · Numerical
A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one…2025 · 24 Jan · Shift 1 · Q56 · MCQ
Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is …2025 · 24 Jan · Shift 2 · Q74 · Numerical
Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:2025 · 28 Jan · Shift 2 · Q61 · MCQ
Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_{A}$ and $R_{B}$ , respectively, with $R_{B} = 2 R_{A}$ . The planet $B$ is $42$ times more massive than planet $A$ . The ratio $(\frac{L _{B}}{L _{A}})$ …2025 · 29 Jan · Shift 2 · Q73 · Numerical
If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = π^{2} m / s^{2}$ , then the length of the second's pendulum at a height $h = 2 R$ from the surface of earth…2024 · 1 Feb · Shift 1 · Q62 · MCQ
A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution T. If the force of attraction between planet and star is proportional to $R^{- 3/2}$ then choose the correct…2024 · 1 Feb · Shift 2 · Q72 · MCQ
A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :2024 · 4 Apr · Shift 1 · Q63 · MCQ
A $90 kg$ body placed at $2 R$ distance from surface of earth experiences gravitational pull of : ( $R =$ Radius of earth, $g = 10 m s^{- 2}$ )2024 · 4 Apr · Shift 2 · Q69 · MCQ
Correct formula for height of a satellite from earths surface is :2024 · 4 Apr · Shift 2 · Q76 · MCQ
If $G$ be the gravitational constant and $u$ be the energy density then which of the following quantity have the dimensions as that of the $uG$ :2024 · 5 Apr · Shift 1 · Q62 · MCQ
Match List I with List II : (Where $a =$ radius of planet orbit, $r =$ radius of planet, $M =$ mass of Sun, $m =$ mass of planet) Choose the correct answer from the options given below : Includes table2024 · 5 Apr · Shift 1 · Q67 · MCQ
A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 1 0^{4} km$ …2024 · 5 Apr · Shift 2 · Q72 · MCQ
To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_{E}, g =$ acceleration due to gravity on the surface of earth):2024 · 6 Apr · Shift 1 · Q68 · MCQ
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be hours 30 minutes.2024 · 6 Apr · Shift 1 · Q82 · Numerical
Assuming the earth to be a sphere of uniform mass density, a body weighed $300 N$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?2024 · 6 Apr · Shift 2 · Q77 · MCQ
Two planets $A$ and $B$ having masses $m_{1}$ and $m_{2}$ move around the sun in circular orbits of $r_{1}$ and $r_{2}$ radii respectively. If angular momentum of $A$ is $L$ and that of $B$ is $3 L$ , the ratio of time period $(\frac{T _{A}}{T _{B}})$ …2024 · 8 Apr · Shift 1 · Q63 · MCQ
Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of $A$ is $3 v$ , the speed of $B$ will be :2024 · 8 Apr · Shift 2 · Q65 · MCQ
An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 km$ . From earth's surface to the orbit, the change in total mechanical energy of the ball is…2024 · 9 Apr · Shift 1 · Q78 · MCQ
A satellite of $1 0^{3} kg$ mass is revolving in circular orbit of radius $2 R$ . If $\frac{1 0 ^{4} R}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g = 10 m / s^{2}, R =$ …2024 · 9 Apr · Shift 2 · Q65 · MCQ
The acceleration due to gravity on the surface of earth is $g$ . If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :2024 · 27 Jan · Shift 1 · Q65 · MCQ
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit…2024 · 27 Jan · Shift 2 · Q66 · MCQ
At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $R$ .)2024 · 29 Jan · Shift 1 · Q66 · MCQ
A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution :2024 · 29 Jan · Shift 2 · Q68 · MCQ
The gravitational potential at a point above the surface of earth is $- 5.12 \times 1 0^{7} J / kg$ and the acceleration due to gravity at that point is $6.4 m / s^{2}$ . Assume that the mean radius of earth…2024 · 30 Jan · Shift 1 · Q80 · MCQ
Escape velocity of a body from earth is $11.2 km / s$ . If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :2024 · 30 Jan · Shift 2 · Q76 · MCQ
A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 m$ , then the time period of small oscillations will be s.…2024 · 30 Jan · Shift 2 · Q88 · Numerical
Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $(\frac{2 2 + 1}{32}) \frac{Gm ^{2}}{L ^{2}}$ , the length of…2024 · 31 Jan · Shift 1 · Q61 · MCQ
The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter is $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is $v$ , the escape velocity on the moon will be :2024 · 31 Jan · Shift 2 · Q79 · MCQ
If earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v _{e}}{3} x ms^{- 1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $P$ , where $v_{e}$ is…2023 · 1 Feb · Shift 1 · Q50 · MCQ
Given below are two statements: Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of…2023 · 1 Feb · Shift 1 · Q55 · MCQ
The escape velocities of two planets $A$ and $B$ are in the ratio $1 : 2$ . If the ratio of their radii respectively is $1 : 3$ , then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of…2023 · 1 Feb · Shift 2 · Q48 · MCQ
For a body projected at an angle with the horizontal from the ground, choose the correct statement.2023 · 1 Feb · Shift 2 · Q59 · MCQ
Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$ . Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere. Reason R : The escape velocity on…2023 · 6 Apr · Shift 1 · Q50 · MCQ
A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:2023 · 6 Apr · Shift 1 · Q54 · MCQ
The weight of a body on the surface of the earth is $100 N$ . The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:2023 · 6 Apr · Shift 2 · Q62 · MCQ
Choose the incorrect statement from the following:2023 · 6 Apr · Shift 2 · Q63 · MCQ
Given below are two statements: Statement I: If $E$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$ . Statement II: The kinetic energy of a satellite revolving in an orbit…2023 · 8 Apr · Shift 1 · Q51 · MCQ
The weight of a body on the earth is $400 N$ . Then weight of the body when taken to a depth half of the radius of the earth will be:2023 · 8 Apr · Shift 1 · Q63 · MCQ
The acceleration due to gravity at height $h$ above the earth if $h << R$ (Radius of earth) is given by2023 · 8 Apr · Shift 2 · Q48 · MCQ
The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new…2023 · 8 Apr · Shift 2 · Q53 · MCQ
Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is2023 · 10 Apr · Shift 1 · Q58 · MCQ
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d = \frac{R}{2}$ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)2023 · 10 Apr · Shift 1 · Q63 · MCQ
If the earth suddenly shrinks to $\frac{1}{64}$ th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}$ h. The value of x is .2023 · 10 Apr · Shift 1 · Q72 · Numerical
The time period of a satellite, revolving above earth's surface at a height equal to $R$ will be (Given $g = π^{2} m / s^{2}, R =$ radius of earth)2023 · 10 Apr · Shift 2 · Q49 · MCQ
Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at…2023 · 10 Apr · Shift 2 · Q54 · MCQ
The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $ρ$ and $ρ /3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_{A} : g_{B})$ will be:2023 · 11 Apr · Shift 1 · Q53 · MCQ
A space ship of mass $2 \times 1 0^{4} kg$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g = 10 m / s^{2}$ …2023 · 11 Apr · Shift 2 · Q56 · MCQ
If $V$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-2023 · 11 Apr · Shift 2 · Q59 · MCQ
The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.2023 · 12 Apr · Shift 1 · Q48 · MCQ
Two satellites $A$ and $B$ move round the earth in the same orbit. The mass of $A$ is twice the mass of $B$ . The quantity which is same for the two satellites will be2023 · 12 Apr · Shift 1 · Q49 · MCQ
A planet having mass $9 Me$ and radius $4 R_{e}$ , where $Me$ and $Re$ are mass and radius of earth respectively, has escape velocity in $km / s$ given by: (Given escape…2023 · 13 Apr · Shift 1 · Q47 · MCQ
Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the…2023 · 13 Apr · Shift 2 · Q45 · MCQ
Two planets A and B of radii $R$ and 1.5 R have densities $ρ$ and $ρ /2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to $A$ is:2023 · 13 Apr · Shift 2 · Q50 · MCQ
Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :2023 · 15 Apr · Shift 1 · Q51 · MCQ
A body is released from a height equal to the radius $(R)$ of the earth. The velocity of the body when it strikes the surface of the earth will be (Given $g =$ acceleration due to gravity on the earth.)2023 · 15 Apr · Shift 1 · Q54 · MCQ
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth $R_{e} = 6400 km$ ) :2023 · 24 Jan · Shift 1 · Q49 · MCQ
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : A pendulum clock when taken to Mount Everest becomes fast. Reason R : The value of g (acceleration due to gravity) is less…2023 · 24 Jan · Shift 2 · Q50 · MCQ
If the distance of the earth from Sun is 1.5 $\times$ 10 $^{6}$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :2023 · 24 Jan · Shift 2 · Q57 · MCQ
Given below are two statements: Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from…2023 · 24 Jan · Shift 2 · Q59 · MCQ
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the…2023 · 25 Jan · Shift 1 · Q54 · MCQ
Every planet revolves around the sun in an elliptical orbit :- A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses of the…2023 · 25 Jan · Shift 2 · Q54 · MCQ
A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R $_{e}$ ), the increase in potential energy will be : (g = acceleration due to gravity on the surface of Earth)2023 · 25 Jan · Shift 2 · Q62 · MCQ
Two particles of equal mass ' $m$ ' move in a circle of radius ' $r$ ' under the action of their mutual gravitational attraction. The speed of each particle will be :2023 · 29 Jan · Shift 1 · Q49 · MCQ
The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.2023 · 29 Jan · Shift 2 · Q56 · MCQ
If the gravitational field in the space is given as $(- \frac{K}{r ^{2}})$ . Taking the reference point to be at $r = 2 cm$ with gravitational potential $V = 10 J / kg$ . Find the…2023 · 30 Jan · Shift 1 · Q54 · MCQ
An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be2023 · 30 Jan · Shift 2 · Q47 · MCQ
At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $3R$ above earth surface. Where $R$ is Radius of earth (Take $R = 6400 km$ …2023 · 31 Jan · Shift 1 · Q55 · MCQ
A body weight $W$ , is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be :2023 · 31 Jan · Shift 2 · Q52 · MCQ
The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is : [Radius of earth R = 6400 km and $3$ = 1.732]2022 · 24 Jun · Shift 1 · Q53 · MCQ
The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :2022 · 24 Jun · Shift 2 · Q47 · MCQ
Three identical particles $A, B$ and $C$ of mass $100 kg$ each are placed in a straight line with $AB = BC = 13 m$ . The gravitational force on a fourth particle $P$ of…2022 · 25 Jul · Shift 1 · Q46 · MCQ
The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = $π$ 2 ms $-$ 2)2022 · 25 Jul · Shift 2 · Q56 · MCQ
An object is taken to a height above the surface of earth at a distance $\frac{5}{4}$ R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :2022 · 25 Jul · Shift 2 · Q58 · MCQ
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).2022 · 25 Jun · Shift 1 · Q48 · MCQ
Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be $\frac{1}{x}$ …2022 · 25 Jun · Shift 2 · Q68 · Numerical
The percentage decrease in the weight of a rocket, when taken to a height of $32 km$ above the surface of earth will, be : $($ Radius of earth $= 6400 km)$ 2022 · 26 Jul · Shift 1 · Q59 · MCQ
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be : (Take radius of earth $= 6400 km$ and $g = 10 ms^{- 2}$ …2022 · 26 Jul · Shift 2 · Q47 · MCQ
The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by : (Given R = radius of earth)2022 · 26 Jun · Shift 1 · Q47 · MCQ
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center…2022 · 26 Jun · Shift 2 · Q51 · MCQ
Two satellites $A$ and $B$ , having masses in the ratio $4 : 3$ , are revolving in circular orbits of radii $3 r$ and $4 r$ respectively around the earth. The ratio of total mechanical energy of…2022 · 27 Jul · Shift 1 · Q52 · MCQ
A body of mass $m$ is projected with velocity $λ v_{e}$ in vertically upward direction from the surface of the earth into space. It is given that $v_{e}$ is escape velocity and$$\lambda(R : radius of…2022 · 27 Jul · Shift 2 · Q46 · MCQ
Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of…2022 · 27 Jun · Shift 1 · Q48 · MCQ
The distance of the Sun from earth is 1.5 $\times$ 1011 m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :2022 · 27 Jun · Shift 2 · Q46 · MCQ
Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is : Includes diagram2022 · 27 Jun · Shift 2 · Q50 · MCQ
If the radius of earth shrinks by $2%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :2022 · 28 Jul · Shift 1 · Q51 · MCQ
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct…2022 · 28 Jun · Shift 1 · Q47 · MCQ
Water falls from a 40 m high dam at the rate of 9 $\times$ 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit,…2022 · 28 Jun · Shift 2 · Q54 · MCQ
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :2022 · 28 Jun · Shift 2 · Q55 · MCQ
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $α h (h << R_{e})$ from the…2022 · 29 Jul · Shift 1 · Q68 · Numerical
An object of mass $1 kg$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $g = 10 ms^{- 2}$ and radius of…2022 · 29 Jul · Shift 2 · Q54 · MCQ
The escape velocity of a body on a planet 'A' is 12 kms $-$ 1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :2022 · 29 Jun · Shift 1 · Q54 · MCQ
The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be2022 · 29 Jun · Shift 2 · Q52 · MCQ
The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3 $ρ$ and 5 $ρ$ respectively. The ratio of their acceleration due to gravity is :2022 · 30 Jun · Shift 1 · Q44 · MCQ
Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is : Includes diagram2021 · 1 Sep · Shift 2 · Q63 · MCQ
Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 $\times$ 103 km. The angular…2021 · 1 Sep · Shift 2 · Q68 · Numerical
The maximum and minimum distances of a comet from the Sun are 1.6 $\times$ 1012 m and 8.0 $\times$ 1010 m respectively. If the speed of the comet at the nearest point is 6 $\times$ 104 ms $-$ 1, the speed at the farthest point is :2021 · 16 Mar · Shift 1 · Q54 · MCQ
If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5} \frac{G M ^{2}}{R}$ where x is (Round off to the…2021 · 16 Mar · Shift 2 · Q65 · Numerical
The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is .2021 · 17 Mar · Shift 1 · Q62 · Numerical
A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R above the surface of 'P', R being the radius of 'P'. The time period of another satellite in hours at a height of 2R from the surface of 'P' is …2021 · 17 Mar · Shift 2 · Q59 · MCQ
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :2021 · 18 Mar · Shift 1 · Q61 · MCQ
If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take g = 10 ms $-$ 2, the radius of earth, R = 6400 $\times$ 103 m, Take $π$ =…2021 · 18 Mar · Shift 2 · Q45 · MCQ
The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $L$ . The magnitude of the areal velocity of the planet is :2021 · 18 Mar · Shift 2 · Q49 · MCQ
A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s2 and 4 m/s2 respectively. Identify from the below… Includes diagram2021 · 20 Jul · Shift 1 · Q62 · MCQ
A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is :2021 · 20 Jul · Shift 2 · Q48 · MCQ
Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA an rB, respectively. If TA and TB are the time period of star A and star B, respectively, Then :2021 · 20 Jul · Shift 2 · Q59 · MCQ
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is s.2021 · 22 Jul · Shift 2 · Q53 · MCQ
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :2021 · 24 Feb · Shift 1 · Q54 · MCQ
Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is :2021 · 24 Feb · Shift 1 · Q55 · MCQ
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :2021 · 24 Feb · Shift 1 · Q60 · MCQ
A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use $g = \frac{GM}{R ^{2}}$ = 9.8 ms $-$ 2 and radius of earth, R = 6400 km.]2021 · 24 Feb · Shift 2 · Q49 · MCQ
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius $(\frac{R}{2})$ is made in the sphere (as shown in figure) and the force becomes… Includes diagram2021 · 25 Feb · Shift 1 · Q47 · MCQ
Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of TB $-$ TA : [Given : radius of earth… Includes diagram2021 · 25 Feb · Shift 1 · Q52 · MCQ
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason R : The product of their mass…2021 · 25 Feb · Shift 1 · Q63 · MCQ
The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that $v_{i} = \frac{x}{y} \times v_{e}$ …2021 · 25 Feb · Shift 2 · Q70 · Numerical
The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet on its trajectory is v0 then its maximum speed will be :2021 · 25 Jul · Shift 1 · Q61 · MCQ
Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :2021 · 25 Jul · Shift 2 · Q55 · MCQ
Inside a uniform spherical shell : (1) the gravitational field is zero (2) the gravitational potential is zero (3) the gravitational field is same everywhere (4) the gravitational potential is same everywhere (5) all of the above Choose…2021 · 26 Aug · Shift 1 · Q46 · MCQ
A planet revolving in elliptical orbit has : A. a constant velocity of revolution. B. has the least velocity when it is nearest to the sun. C. its areal velocity is directly proportional to its velocity. D. areal velocity is inversely…2021 · 26 Feb · Shift 1 · Q57 · MCQ
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $8$ R is the distance between the centres of a ring (of… Includes diagram2021 · 26 Feb · Shift 1 · Q62 · MCQ
In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is … Includes diagram2021 · 26 Feb · Shift 2 · Q74 · Numerical
A body of mass (2M) splits into four masses (m, M $-$ m, m, M $-$ m}, which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is x… Includes diagram2021 · 27 Aug · Shift 1 · Q59 · Numerical
A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :2021 · 27 Aug · Shift 2 · Q49 · MCQ
Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M'… Includes diagram2021 · 27 Jul · Shift 1 · Q67 · Numerical
Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :2021 · 27 Jul · Shift 2 · Q56 · MCQ
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $\times$ 103 km. Find the mass of Mars. ${G i v e n \frac{4 π ^{2}}{G} = 6 \times 10^{11} N^{- 1} m^{- 2} k g^{2}}$ …2021 · 27 Jul · Shift 2 · Q60 · MCQ
The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :2021 · 31 Aug · Shift 1 · Q52 · MCQ
If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given : r < RE)2021 · 31 Aug · Shift 2 · Q62 · MCQ
The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as :2020 · 2 Sep · Shift 1 · Q44 · MCQ
The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)2020 · 2 Sep · Shift 2 · Q48 · MCQ
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion…2020 · 3 Sep · Shift 1 · Q57 · MCQ
The mass density of a planet of radius R varies with the distance r from its centre as $ρ$ (r) = $ρ_{0} (1 - \frac{r ^{2}}{R ^{2}})$ . Then the gravitational field is maximum at :2020 · 3 Sep · Shift 2 · Q62 · MCQ
On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by $\frac{A x}{( x ^{2} + a ^{2} ) ^{3/2}}$ in the x-direction. The magnitude of gravitational potential on the…2020 · 4 Sep · Shift 1 · Q45 · MCQ
A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:2020 · 4 Sep · Shift 2 · Q63 · MCQ
The value of the acceleration due to gravity is g1 at a height h = $\frac{R}{2}$ (R = radius of the earth) from the surface of the earth. It is again equal to g1 at a depth d below the surface of the earth. The ratio $(\frac{d}{R})$ …2020 · 5 Sep · Shift 1 · Q60 · MCQ
The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth about the axis passing through the pole is $ω$ . An object is weighed at the equator and at a height h above the poles by using…2020 · 5 Sep · Shift 2 · Q42 · MCQ
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the…2020 · 6 Sep · Shift 1 · Q53 · MCQ
Two planets have masses M and 16 M and their radii are $a$ and 2 $a$ , respectively. The separation between the centres of the planets is 10 $a$ . A body of mass m is fired from the surface of the larger planet towards the smaller planet…2020 · 6 Sep · Shift 2 · Q54 · MCQ
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 $\frac{m}{10}$ so that subsequently the satellite…2020 · 7 Jan · Shift 1 · Q54 · MCQ
A box weight 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 ms–2 at the north pole and the radius of the earth = 6400 km) :2020 · 7 Jan · Shift 2 · Q43 · MCQ
Consider two solid spheres of radii R1 = 1m, R2 = 2m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M _{1}}{M _{2}}$ is : Includes diagram2020 · 8 Jan · Shift 1 · Q46 · MCQ
An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (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…2020 · 8 Jan · Shift 2 · Q57 · Numerical
A ball is dropped from the top of a 100 m high tower on a planet. In the last $\frac{1}{2} s$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms–2) near the surface on that planet is …2020 · 8 Jan · Shift 2 · Q59 · Numerical
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 $(\frac{v}{2})$ the instantaneous velocity $v$ …2020 · 9 Jan · Shift 1 · Q60 · MCQ
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 vA and vB, respectively, then $\frac{v _{A}}{v _{B}} = \frac{n}{4}$ . The value of n is :2020 · 9 Jan · Shift 2 · Q49 · MCQ
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? Includes diagram2019 · 8 Apr · Shift 1 · Q55 · MCQ
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched…2019 · 8 Apr · Shift 2 · Q67 · MCQ
A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be :2019 · 9 Apr · Shift 1 · Q63 · MCQ
A test particle is moving in a circular orbit in the gravitational field produced by a mass density $ρ (r) = \frac{K}{r ^{2}}$ . Identify the correct relation between the radius R of the particle's orbit and its period T2019 · 9 Apr · Shift 2 · Q53 · MCQ
The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 $\times$ 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for…2019 · 9 Jan · Shift 2 · Q64 · MCQ
The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms–2, is close to : (Radius of earth = 6.4 × 106 m)2019 · 10 Apr · Shift 1 · Q45 · MCQ
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…2019 · 10 Apr · Shift 2 · Q53 · MCQ
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…2019 · 10 Jan · Shift 1 · Q63 · MCQ
Two stars of masses 3 $\times$ 1031 kg each, and at distance 2 $\times$ 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from…2019 · 10 Jan · Shift 2 · Q66 · MCQ
A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so…2019 · 11 Jan · Shift 1 · Q66 · MCQ
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?…2019 · 12 Apr · Shift 2 · Q64 · MCQ
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 inelastically. The speeds of the satellite and the…2019 · 12 Jan · Shift 1 · Q49 · MCQ
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 + Bx2 , is given by :2019 · 12 Jan · Shift 1 · Q51 · MCQ
Two satellites, A and B, have masses m and 2m 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, TA/TB, is ;2019 · 12 Jan · Shift 2 · Q64 · MCQ
Take the mean distance of the moon and the sun from the earth to be $0.4 \times 1 0^{6}$ km and $150 \times 1 0^{6}$ km respectively. Their masses are $8 \times 1 0^{22}$ kg and $2 \times 1 0^{30}$ kg respectively. The radius of the earth…2018 · 15 Apr · Shift 1 · Q64 · MCQ
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…2018 · 15 Apr · Shift 1 · Q67 · MCQ
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :2018 · 16 Apr · Shift 1 · Q65 · MCQ
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then :2018 · Shift 0 · Q59 · MCQ
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4}$ W. Radius of the…2017 · 8 Apr · Shift 1 · Q71 · MCQ
The mass density of a spherical body is given by $ρ$ (r) = $\frac{k}{r}$ for r $\leq$ R and $ρ$ (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…2017 · 9 Apr · Shift 1 · Q56 · MCQ
The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by (R = Earth’s radius):2017 · Shift 0 · Q60 · MCQ
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 semimajor axis, and ca as the semiminor axis. If t1 is the time taken… Includes diagram2016 · 9 Apr · Shift 1 · Q49 · MCQ
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 :2016 · 10 Apr · Shift 1 · Q58 · Multiple correct
A satellite is revolving 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…2016 · Shift 0 · Q60 · MCQ
From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R /2$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the center of the cavity thus formed is: ( $G = g r a v i t a t i o na l co n s t an t$ … Includes diagram2015 · Shift 0 · Q61 · MCQ
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 :2014 · Shift 0 · Q69 · MCQ
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 $2 R$ ?2013 · Shift 0 · Q71 · MCQ
The mass of a spaceship is $1000 k g .$ 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 $6400 k m$ respectively. The required energy for this work will be:2012 · Shift 0 · Q57 · MCQ
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:2011 · Shift 0 · Q73 · MCQ
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:2009 · Shift 0 · Q73 · MCQ
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 $11 k m s^{- 1},$ the escape velocity from the surface of the planet…2008 · Shift 0 · Q70 · MCQ
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 center of a cube of side $^{'} a^{'}$ ,…2008 · Shift 0 · Q82 · MCQ
If $g_{E}$ and $g_{M}$ 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 $\frac{e l ec t r o c h a r g e o n t h e m oo n}{e l ec t r o ni c c h a r g e o n t h e e a r t h} t o b e$ …2007 · Shift 0 · Q79 · MCQ
Average density of the earth2005 · Shift 0 · Q143 · MCQ
A particle of mass $10 g$ is kept on the surface of a uniform sphere of mass $100 k g$ and radius $10 c m .$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 1 0^{- 11} N m^{2} / k g^{2}$ …2005 · Shift 0 · Q167 · MCQ
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…2005 · Shift 0 · Q183 · MCQ
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 is2004 · Shift 0 · Q165 · MCQ
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 is2004 · Shift 0 · Q166 · MCQ
The time period of an earth satellite in circular orbit is independent of2004 · Shift 0 · Q167 · MCQ
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 to2004 · Shift 0 · Q168 · MCQ
The time period of satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become2003 · Shift 0 · Q149 · MCQ
Two spherical bodies of mass $M$ and $5 M$ & radii $R$ & $2 R$ respectively are released in free space with initial separation between their centers equal to $12 R$ . If they attract each other due to gravitational force only, then the…2003 · Shift 0 · Q150 · MCQ
The escape velocity for a body projected vertically upwards from the surface of earth is $11 k m / s .$ If the body is projected at an angle of $4 5^{\circ}$ with the vertical, the escape velocity will be2003 · Shift 0 · Q151 · MCQ
The escape velocity of a body depends upon mass as2002 · Shift 0 · Q142 · MCQ
The kinetic energy needed to project a body of mass $m$ from the earth surface (radius $R$ ) to infinity is2002 · Shift 0 · Q166 · MCQ
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will2002 · Shift 0 · Q183 · MCQ
Energy required to move a body of mass $m$ from an orbit of radius $2 R$ to $3 R$ is2002 · Shift 0 · Q184 · MCQ