Gravitation

A body of mass \(\mathrm{m}\) is projected with velocity \(\lambda \,v_{\mathrm{e}}\) in vertically upward direction from the surface of the earth into space. It is given that \(v_{\mathrm{e}}\) is escape velocity and \(\lambda<1\). If air ...

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)

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 of...

The percentage decrease in the weight of a rocket, when taken to a height of \(32 \mathrm{~km}\) above the surface of earth will, be :
\((\) Radius of earth \(=6400 \mathrm{~km})\)

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 \(=6400 \mathrm{~km}\) and $$\mathrm{g}=10 \math...

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).

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 $${1 \over x...

Three identical particles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of mass \(100 \mathrm{~kg}\) each are placed in a straight line with \(\mathrm{AB}=\mathrm{BC}=13 \mathrm{~m}\). The gravitational force on a fourth particle $$\mathrm{...

An object is taken to a height above the surface of earth at a distance \({5 \over 4}\) 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 :

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 = \(\pi\)2 ms\(-\)2)

The approximate height from the surface of earth at which the weight of the body becomes \({1 \over 3}\) of its weight on the surface of earth is :
[Radius of earth R = 6400 km and \(\sqrt 3\) = 1.732]

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

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 :

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)

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' direct...

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.$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \...

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 :

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 \({M \over m}\) for which, the gravitational potential energy of the system becomes maximum...

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 :

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 \(\sqrt 8\)R is the distance between the centres of a ring (of...

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 proportio...

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 ________.

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 aboveChoose the most ...

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 :

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 :

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 \(\left( {{R \over 2}} \right)\) is made in the sphere (as shown in figure) and the force becomes ...

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 and r...

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 ...

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} = \sqrt {{x \...

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 :

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 :

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 :

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 \(g = {{GM} \over {{R^2}}}\) = 9.8 ms\(-\)2 and radius of earth, R = 6400 km.]

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.

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...

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 :

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 :

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 ...

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 :

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 :

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 \(\pi\) = ...

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is \({\overrightarrow L }\). The magnitude of the areal velocity of the planet is :

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 ___________.

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 ________...

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 :

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 \({x \over 5}{{G{M^2}} \over R}\) where x is __________ (Round off to the Nearest Integer...

A body A of mass m is moving in a circular orbit
of radius R about a planet. Another body B of
mass
\({m \over 2}\)
collides with A with a velocity which is half \(\left( {{{\overrightarrow v } \over 2}} \right)\) the instantaneous velocity...

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 \({{{v_A}} \over {{v_B}}} = {n \over 4}\).
The value of n is :

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 \({{{M_1}} \over {{M_2}}}\) is :

A ball is dropped from the top of a 100 m high
tower on a planet. In the last \({1 \over 2}s\) 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 _____.