Gravitation

The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is:

[NEET 2024]

The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

[Re-NEET 2024]

The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

[NEET 2025]

The mass of a planet is \({\left(\frac{1}{10}\right)}^{th}\) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on the surface of that planet is:

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 is equal to the half the magnitude of total energy \(E\). In the light of the above statements, choose the most appropriate answer from the options given below

[JEE Main 2023, 8 Apr (Shift 1)]

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 at Mount Everest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below

[JEE Main 2023, 24 Jan (Shift 2)]

A geostationary satellite is orbiting around an arbitrary planet \(P\) at a height of \(11 R\) above the surface of \(P\), \(R\) being the radius of \(P\). The time period of another satellite in hours at a height of \(2 R\) from the surface of \(P\) is ________.

\(P\) has the time period of 24 hours.

[JEE Main 2021, 17 Mar (Shift 2)]

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)

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:

[JEE Main 2023, 8 Apr (Shift 1)]

\(T\) is the time period of a simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the surface of earth. Then, the value of \(x\) will be:

[JEE Main 2023, 25 Jan (Shift 1)]

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

[JEE Main 2023, 6 Apr (Shift 1)]

If earth has a mass nine times and radius twice that of a planet \(P\). Then \(\frac{v_e}{3} \sqrt{x} m^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(P\), where \(v_e\) is escape velocity on earth. The value of \(x\) is

[JEE Main 2023, 1 Feb (Shift 1)]

Assertion (A): A simple pendulum is taken to a planet of mass 4 times that of Earth and radius 2 times that of Earth; the time period remains constant.

Reason (R): The time period of a simple pendulum is constant on Earth and any other planet.

(Shift II Memory Based)

The escape velocity from the Earth's surface is \( v \). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

[NEET 2021]

Every planet revolves around the sun in an elliptical orbit:
A. The force acting on a planet is inversely proportional to square of the distance from the sun.
B. Force acting on a planet is inversely proportional to the product of the masses of the planet and the sun C.
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below:

[JEE Main 2023, 25 Jan (Shift 2)]

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity \(\frac{3\pi }{\mathrm{Gd}}\) represents :

[NEET 2023]

A planet having mass \(9 M_e\) and radius \(4 R_e\), where \(M_e\) and \(R_e\) are mass and radius of earth respectively, has escape velocity in \(km / s\) given by
(Given escape velocity on earth \(v_e=11.2 \times 10^3 m / s\) )

[JEE Main 2023, 13 Apr (Shift 1)]

Inside a uniform spherical shell :
(A) the gravitational field is zero
(B) the gravitational potential is zero
(C) the gravitational field is same everywhere
(D) the gravitation potential is same everywhere
(E) all the above

Choose the correct answer from the options given below :

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 proportional to its velocity.
E. To follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below:

[JEE Main 2021, 26 Feb (Shift 1)]

A body weighs \( 72 \mathrm{~N} \) on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

[NEET 2020]

Choose the incorrect statement from the following:

A particle of mass \( \mathrm{m} \) is projected with a velocity \( \mathrm{v}=\mathrm{kV_e}(\mathrm{k}<1) \) from the surface of the earth. The maximum height above the surface reached by the particle is:

[NEET 2021]

A spaceship of mass \(2 \times 10^4 kg\) is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if \(g=10 m / s ^2\) and radius of earth \(=6400 km )\)

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 be:

The depth \( d \) at which the value of acceleration due to gravity becomes \( 1 / n \) times the value at the surface, is \( [R= \) radius of the earth]

[Re-NEET 2020]