Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given: M = 6.4 × 1024 kg, R = 3.4 × 106 m, m = 800 kg
To find: Energy required to remove the object from the surface of planet to infinity = B.E.
Formula: B.E. = `"GMm"/"R"`
Calculation: We know that,
G = 6.67 × 10–11 N m2/kg2
From formula,
B.E. = `(6.67 xx 10^-11 xx 6.4 xx 10^24 xx 800)/(3.4 xx 10^6)`
∴ B.E. =`(6.67 xx 6.4 xx 8)/3.4 xx 10^9`
∴ B.E. = 100.44 × 109 J
Energy required to remove the object from the surface of the planet is 1.004 × 1011 J.
Notes
The Answer given in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east one to west and the other from west to east. Will they have the same time period as seen from the earth? If not which one will have less time period?
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 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
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
A Mars satellite moving in an orbit of radius 9.4 × 103 km takes 27540 s to complete one revolution. Calculate the mass of Mars.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
Choose the correct option.
The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 109 J. It's kinetic energy is ______.
Answer the following question.
Why is a minimum two-stage rocket necessary for launching of a satellite?
Derive an expression for the critical velocity of a satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Answer the following question in detail.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
Solve the following problem.
Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
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?
The ratio of energy required to raise a satellite of mass 'm' to a height 'h' above the earth's surface of that required to put it into the orbit at same height is ______.
[R = radius of the earth]
Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter is ______
Which of the following statements is CORRECT in respect of a geostationary satellite?
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 a body weighing 40 kg-wt is taken inside the earth to a depth to `1/2` th radius of the earth, then the weight of the body at that point is ____________.
A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is ______.
Is it possibe for a body to have inertia but no weight?
Show the nature of the following graph for a satellite orbiting the earth.
- KE vs orbital radius R
- PE vs orbital radius R
- TE vs orbital radius R.
An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface ______ km/s.
[g = 9.8 ms-2 and Re = 6400 km]
Two satellites of same mass are orbiting round the earth at heights of r1 and r2 from the centre of earth. Their potential energies are in the ratio of ______.
Which of the following is the only natural satellite of the Earth?
