Gravitation

The acceleration due to gravity at height \(h\) above the earth if \(h << \mathrm{R}\) (Radius of earth) is given by

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing \(\mathrm{W}\) on earth will weigh on that planet:

Given below are two statements : one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\).
Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere.
Reason R : The escape velocity on ...

Choose the incorrect statement from the following:

The weight of a body on the surface of the earth is \(100 \mathrm{~N}\). 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:

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 \(\mathrm{3 R}\) above earth surface. Where \(\mathrm{R}\) is Radius of earth (Take $$\mathrm{R}=6400 \mat...

A body weight $\mathrm{W}$, 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 :

If the gravitational field in the space is given as \(\left(-\frac{K}{r^{2}}\right)\). Taking the reference point to be at \(\mathrm{r}=2 \mathrm{~cm}\)
with gravitational potential \(\mathrm{V}=10 \mathrm{~J} / \mathrm{kg}\). Find the gra...

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 be

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 :

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.

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 parti...

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)

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 pla...

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 \(\mathrm{R_e=6400~km}\)) :

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 earth's...

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 :

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 a...

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 ...

If earth has a mass nine times and radius twice to that of a planet P. Then \(\frac{v_{e}}{3} \sqrt{x} \mathrm{~ms}^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(\mathrm{P}\), where $$v_{e}...

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

The escape velocities of two planets \(\mathrm{A}\) and \(\mathrm{B}\) 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...

A body is released from a height equal to the radius $(\mathrm{R})$ 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.)

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 :

A planet having mass \(9 \mathrm{Me}\) and radius \(4 \mathrm{R}_{\mathrm{e}}\), where \(\mathrm{Me}\) and \(\mathrm{Re}\) are mass and radius of earth respectively, has escape velocity in \(\mathrm{km} / \mathrm{s}\) given by:
(Given escap...

Two planets A and B of radii \(\mathrm{R}\) and 1.5 R have densities \(\rho\) and \(\rho / 2\) respectively. The ratio of acceleration due to gravity at the surface of \(\mathrm{B}\) to \(\mathrm{A}\) is:

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 p...

Two satellites \(\mathrm{A}\) and \(\mathrm{B}\) move round the earth in the same orbit. The mass of \(\mathrm{A}\) is twice the mass of \(\mathrm{B}\). The quantity which is same for the two satellites will be

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.

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \(\rho\) and \(\rho / 3\) respectively. The ratio of acceleration due to gravity at their surfaces \(\left(g_{A}: g_{B}\right)\) will be:

If \(\mathrm{V}\) 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:-

A space ship of mass \(2 \times 10^{4} \mathrm{~kg}\) 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 ...

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 __________.

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)

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 is

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 th...

The time period of a satellite, revolving above earth's surface at a height equal to \(\mathrm{R}\) will be
(Given \(g=\pi^{2} \mathrm{~m} / \mathrm{s}^{2}, \mathrm{R}=\) radius of earth)

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3\(\rho\) and 5\(\rho\) respectively. The ratio of their acceleration due to gravity is :

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 :

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 be

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 \(\alpha \mathrm{h}\left(\mathrm{h}<<\mathrm{R}_{\mathrm{e}}\right)\) from...

An object of mass \(1 \mathrm{~kg}\) 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, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) and radius of...

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 relat...

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 :

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...

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 :

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 the...

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 :

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 :

Two satellites \(\mathrm{A}\) and \(\mathrm{B}\), having masses in the ratio \(4: 3\), are revolving in circular orbits of radii \(3 \mathrm{r}\) and \(4 \mathrm{r}\) respectively around the earth. The ratio of total mechanical energy of $$...