Advertisements
Advertisements
प्रश्न
Solve the following problem.
What is the gravitational potential due to the Earth at a point which is at a height of 2RE above the surface of the Earth?
(Mass of the Earth is 6 × 1024 kg, radius of the Earth = 6400 km and G = 6.67 × 10–11 N m2 kg–2)
Advertisements
उत्तर
Given: M = 6 × 1024 kg, RE = 6400 km = 6.4 × 106 m, G = 6.67 × 10–11 N m2/kg2, h = 2RE
To find: Gravitational potential (V)
Formula: V = -`"GM"/"r"`
Calculation: From formula,
V = `- "GM"/("R"_"E" + 2"R"_"E")`
`= - (6.67 xx 10^-11 xx 6 xx 10^24)/(3 xx 6.4 xx 10^6)`
`= -(6.67 xx 2)/6.4 xx 10^7`
= - 2.08 × 107 J kg-1
Negative sign indicates the attractive nature of gravitational potential.
Gravitational potential due to Earth will be 2.08 × 107 J kg-1 towards the centre of the Earth.
APPEARS IN
संबंधित प्रश्न
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
(a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation. (b) If the satellite is directly above the North Pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth = 6 × 1024 kg.
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Answer the following question.
Define the binding energy of a satellite.
Derive an expression for the critical velocity of a satellite.
Answer the following question in detail.
State any four applications of a communication satellite.
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Solve the following problem.
Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
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?
Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbit of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2?
Reason of weightlessness in a satellite 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 ____________.
Assuming that the earth is revolving around the sun in circular orbit of radius 'R', the angular momentum is directly proportional to rn. The value of 'n' is ______.
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 ______.
In the case of earth, mean radius is 'R', acceleration due to gravity on the surface is 'g', angular speed about its own axis is 'ω'. What will be the radius of the orbit of a geostationary satellite?
The period of revolution of a satellite 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?
What is the typical altitude range for a polar satellite's orbit?
Artificial satellites are launched for all the following purposes EXCEPT ______.
