Chapter Test: Gravitation - 1 JEE Physics Free MCQs

With what angular velocity the earth should spin in order that a body lying at 45° latitude may become weightless ?

A particle is projected with velocity kve in vertically upward direction from the ground into the space (v_e is escape velocity & k < 1) then the maximum height from the centre of earth to which it can go, will be -

A planet revolves in elliptical orbit around the sun. The linear speed of the planet will be maximum at :

A projectile is fired from the surface of earth of radius R with a velocity η v_e where v_e is the escape velocity and η<1. Neglecting air resistance, the orbital velocity of projectile is -

The diameters of two planets are in the ratio of 4 : 1 & mean density have ratio 1 : 2, then the ratio of g on the planets will be -

A particle is kept at rest at a distance R (Earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is :

The value of g on the surface of earth is 9.8 m/s² & the radius of earth is 6400 km. The avg. density of earth in kg/m³ will be -

With what angular velocity the earth should spin in order that a body lying at 45º latitude may become weightless ?

A body is projected up with a velocity equal to (3/4)th of the escape velocity from the surface of the earth. The height it reaches is-

(Radius of earth = R)

A, B, C and D are four masses each of mass M lying on the vertices of a square of side 'a'. They always move along a common circle with velocity v. Find v so that they always remain on the vertices of the square -

Consider a very long stick of length 2R, which extends from just above the surface of the earth, to a radius 3R. If initial conditions have been set up so that this stick moves in a circular orbit while always pointing radially. What is the period of this orbit. g represents acceleration due to gravity on surface of earth.

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to -

A satellite is revolving round the earth with orbital speed v₀. If it is imagined to stop suddenly, the speed with which it will strike the surface of the earth would be (v_e - escape speed of a body from earth’s surface)

In the asteroid belt, a pebble is in close orbit around a spherical rock having density nearly same as that of earth. ("Close," meaning that the pebble goes around the rock very near to the rock's surface). Orbital period of the pebble around the rock is of the order of

The time period of a 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 become -

A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be -

A point mass m₀ is placed at distance R/3 from the centre of a spherical shell of mass m and radius R. The gravitational force on the point mass m₀ is -

The correct graph representing the variation of total energy(E), kinetic energy(K) & potential energy (u) of a satellite with its distance from the centre of earth is -

Two bodies of masses m₁ and m₂ are initially at rest placed infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity when they are r distance apart is –

If the radius of earth were shrink by 1%, its mass remaining th same, the acceleration due to gravity on the earth's surface would -

The gravitational potential at height h above the earth's surface is – 5.12 × 10⁷ J/kg and acceleration due to gravity at this point is 6.4 m s². If radius of the earth is 6400 km, the value of h is :

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

The escape velocity for a planet is v_e. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

Two uniform spherical stars made of same material have radii R and 2R. Mass of the smaller planet is m. They start moving from rest towards each other from a large distance under mutual force of gravity. The collision between the stars is inelastic with coefficient of restitution 1/2.

Kinetic energy of the system just after the collision is

A mass is at the center of a square, with four masses at the corners as shown.

(A)  (B) 

(C)  (D) 

Rank the choices according to the magnitude of the gravitational force on the center mass.

A geostationary satellite is at a height h above the surface of earth. If earth radius is R

For a satellite to orbit around the earth, which of the following must be true ?