If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is , here G is gravitational constant
The relation between G and K is described as:
A remote-sensing satellite of the Earth revolves in a circular orbit at a height of 0.25 ✕ 106 m above the surface of the Earth. If the Earth's radius is 6.38 ✕ 106 m and g = 9.8 ms−2, then the orbital speed of the satellite is
(G = gravitational constant)
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?
Reason Potential energy of the body at a point in the orbit is .
Reason This is because g = 0 at the centre of earth.
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8m, ……, respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:
The height at which the weight of a body becomes 1/16 th , its weight on the surface of earth (radius R), is :
A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to:
Two spherical planets P and Q have the same uniform density ρ masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is (MP + MQ).The escape velocities from the planets P, Q, and R, are VP, VQ and VR, respectively. Then
A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ’m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is
Reason : Rotation of earth is about polar axis.
A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
Gravitational acceleration on the surface of a planet is , where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 km/s, the escape speed on the surface of the planet in km/s will be
(Radius of the earth is 6400 km)