Advertisements
Advertisements
प्रश्न
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
Advertisements
उत्तर
- Let,
M = mass of the Earth
m = mass of the satellite
R = radius of the Earth. - Since the satellite is at rest on the Earth, v = 0
∴ Kinetic energy of satellite,
K.E. = `1/2 "mv"^2 = 0` - Gravitational potential at the Earth’s surface = `- "GM"/"R"`
∴ The potential energy of a satellite = Gravitational potential × mass of the satellite
= `-"GMm"/"R"` - Total energy of satellite = T.E = P.E + K.E
∴ T.E. = `-"GMm"/"R" + 0 = "GMm"/"R"` - A negative sign in the energy indicates that the satellite is bound to the Earth due to the gravitational force of attraction.
- For the satellite to be free from Earth’s gravitational influence, its total energy should become positive. That energy is the binding energy of the satellite at rest on the surface of the Earth.
∴ B.E. = `"GMm"/"R"`
APPEARS IN
संबंधित प्रश्न
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve. Its speed with respect to the satellite
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
Answer the following question in detail.
State any four applications of a communication satellite.
Answer the following question in detail.
What is a critical velocity?
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
A planet has mass 6.4 × 1024 kg and radius 3.4 × 106 m. Calculate the energy required to remove an object of mass 800 kg from the surface of the planet to infinity.
A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
Which of the following statements is CORRECT in respect of a geostationary satellite?
Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3v, the speed of satellite B is ____________.
A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth. R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is ____________.
If the Earth-Sun distance is held constant and the mass of the Sun is doubled, then the period of revolution of the earth around the Sun will change to ____________.
Out of following, the only correct statement about satellites is ____________.
The ratio of energy required to raise a satellite to a height `(2R)/3` above earth's surface to that required to put it into the orbit at the same height is ______.
R = radius of the earth
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is ______.
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.
Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because ______.
Is it possibe for a body to have inertia but no weight?
A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is ______.
A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?
A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.
(G = universal constant of gravitation)
A satellite is revolving round the earth with orbital speed ‘V0’. If it stops suddenly, the speed with which it will strike the surface of the earth would be: (V = escape velocity of a particle on earth’s surface)
