AIIMS Physics Gravitation Class 11 Questions

If radius of the earth is 6347 km, then what will be difference between acceleration of free fall and acceleration due to gravity near the earth's surface?

Find the gravitational field at a distance of 2000 km from centre of earth. (Given Rₑₐᵣₜₕ = 6400 km, r = 2000 km, Mₑₐᵣₜₕ = 6 × 10²⁴ kg);

A planet has same density as that of earth and universal gravitational constant $G$ is twice that of earth, the ratio of acceleration due to gravity, is.

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and a radius of 10 cm. 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 = 6.67×10⁻¹¹ Nm²/kg²)

Assertion: When the lift moves with uniform velocity the man in the lift will feel weightlessness. Reason: In downward accelerated motion of lift, apparent weight of a body increases.

Assertion: Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points.

Reason: Gravitational forces are conservative forces.

The gravitational field in a region is given by $\vec{g} = 5\text{ N/kg}\hat{i} + 12\text{ N/kg}\hat{j}$. The change in the gravitational potential energy of a particle of mass $1\text{ kg}$ when it is taken from the origin to a point $(7\text{ m}, -3\text{ m})$ is:

The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold its present value and all other things remain unchanged, the period of moon’s rotation would be nearly

Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length $a$. Their common time period will be

Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places. Reason: The value of acceleration due to gravity depends upon the rotation of the earth.

Assertion : Water kept in an open vessel will quickly evaporate on the surface of the moon.

Reason : The temperature at the surface of the moon is much higher than boiling point of the water.

Assertion: The gain in potential energy of an object of mass m raised to height equal to the radius of earth is $\frac{1}{2} mgR$.

Reason Statement:Kinetic energy at top $\frac{1}{2}mv^2$ = P.E. at the top and at the top, $v = \sqrt{gR}$.$\therefore \text{PE} = \frac{1}{2}mgR$

Consider a planet in solar system which has the mass double mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weight

The escape velocity from the earth is about 11 $kms ^{-1}$.The escape velocity from a planet having twice he radius and the same mean density as the earth is

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the Earth=R)

Two satellites S₁ and S₂ are revolving around a planet in coplanar circular orbits of radius r₁ and r₂ in the same direction, respectively. Their respective periods of revolution are 1h and 8h. The radius of orbit of satellite S₁ is equal to 10⁴ km. What will be their relative speed (in km/h) when they are closest?

Time period of pendulum, on a satellite orbiting the earth, is

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer from a circular orbit of radius R₁ to another of radius R₂(R₂ > R₁) is

The reading of a spring balance corresponds to 100 N while situated at the north pole and a body is kept on it. The weight record on the same scale if it is shifted to the equator, is (take, g = 10 m/s² and radius of the earth, R = 6.4 × 10³ m)

Assertion (A) An astronaut in an orbiting space station above the earth experience weightlessness.

Reason (R) An object moving around the earth under the influence of earth’s gravitational force is in a state of ‘free fall’.

Gravitational potential of the body of mass m at a height h from surface of earth of radius R is [Take g = acceleration due to gravity at earth's surface]

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

A particle is thrown vertically upwards with velocity 11.2 km s⁻¹ from the surface of earth. Calculate its velocity at height 3 R. Where R is the radius of earth.

Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude, due to rotation of earth

Assertion: Total energy is conserved in moving a satellite to higher orbit. Reason: Sum of change in PE and KE is same in magnitude and opposite in nature.

Assertion : The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth. Reason : The value of acceleration due to gravity is minimum at the equator and maximum at the pole.

A wire of length l and mass m is bent in the form of a semicircle. The gravitational field intensity at the centre of semicircle is

Assertion : Angular speed of a planet around the sun increases, when it is closer to the sun. Reason : Total angular momentum of the system remains constant.

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 to

Figure shows the variation of energy with the orbit radius r of a satellite in a circular motion. Mark the correct statement.

Height of geostationary satellite is

Assertion : An astronaut experience weightlessness in a space satellite.

Reason : When a body falls freely it does not experience gravity.

Assertion : A man in a closed cabin which is falling freely does not experience gravity.

Reason : Inertial and gravitational mass have equivalence.

The condition for a uniform spherical mass m of radius r to be a black hole is [G = gravitational constant and g = acceleration due to gravity]

The velocity with which a projectile must be fired so that it escapes earth's gravitation does not depend on

The motion of planets in the solar system is an example of the conservation of

Assertion : The length of the day is slowly increasing.

Reason : The Coulomb force is weaker than the gravitational force.

Assertion : The length of the day is slowly increasing.

Three different objects m₁, m₂ and m₃ are allowed to fall from rest and from the same point O along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of

The force of gravitation is

Kepler's second law is based on

If v₀ be the orbital velocity of a satellite in a circular orbit close to the earth's surface and vₑ is the escape velocity from the earth, then relation between the two is

The orbital velocity of an artificial satellite in a circular orbit above the earth's surface at a distance equal to radius of earth is v. For a satellite orbiting at an altitude half of earth's radius, orbital velocity is

Escape velocity of a rocket is 11.2 km/sec. It is released at an angle of 45°. Its escape velocity is

A body weighed 250 N on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh half way down to the centre of the earth?

What is the dimensional formula for the gravitational constant?

Assertion (A): At pole value of acceleration due to gravity (g) is greater than that of equator.

Reason (R): Earth rotates on its axis in addition to revolving round the sun.

Assertion (A): The time period of revolution of a satellite around a planet is directly proportional to the radius of the orbit of the satellite.

Reason (R): Artificial satellite do not follow Kepler's laws of planetary motion.

What is the dimensional formula of gravitational constant G?

Knowing that mass of Moon is M/81 where M is the mass of Earth, find the distance of the point where gravitational field due to Earth and Moon cancel each other, from the Moon. Given that distance between Earth and Moon is 60 R, where R is the radius of Earth.