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Two identical satellites are at R and 7R away from earth's surface, the wrong statement is (R= radius of the earth)

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Important Questions on Gravitation

EASY
A body is projected upwards with a velocity of 4×11.2 km s-1 from the surface of earth. The velocity of the body when it escapes the gravitational pull of earth is
EASY
A satellite is orbiting close to the earth and has a kinetic energy K. The minimum extra kinetic energy required by it to just overcome the gravitation pull of the earth is
EASY
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
MEDIUM
Define binding energy and obtain an expression for binding energy of a satellite revolving in a circular orbit round the earth.
MEDIUM
A satellite of mass m is orbiting the earth (of radius R ) at a height h from its surface. The total energy of the satellite in terms of g o , the value of acceleration due to gravity at the earth's surface, is
HARD

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.

EASY
Binding energy of a revolving satellite at height h is 3.5×108 J. Its potential energy is
EASY

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  E2.

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.

EASY
The ratio of the binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is (R= radius of the earth).
EASY
A satellite is orbiting the Earth in a circular orbit of radius R . Which one of the following statements is true?
MEDIUM
State Kepler’s law of orbit and law of equal areas.
MEDIUM
The energy required to take a satellite to a height h above the Earth surface (radius of Earth =6.4×103 km ) is E1, and the kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for which E1 and E2 are equal, is
MEDIUM
A satellite is orbiting round the earth in a circular orbit with speed ν. If m is mass of satellite, its total energy is
HARD

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet. The minimum speed v required for the satellite to reach the surface of the second planet is a7GMR, then the value of  a is
[Given : The two planets are fixed in their position]

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MEDIUM
Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is 
HARD
A body is thrown from the surface of the earth with velocity u m s-1. The maximum height in meter above the surface of the earth up to which it will reach is (R= radius of the earth, g= acceleration due to gravity)
MEDIUM
The kinetic energies of a planet in an elliptical orbit about the Sun, at positions, A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shows in the figure. Then

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HARD
An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the centre of the earth, it has a speed of 12 km s-1. Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km s-1) ? Give your answer to the nearest integer in km s-1__________.
MEDIUM
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R ?
MEDIUM
Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, KAKB is: