Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given: M = 6 × 1024 kg, R = 6400 km = 6.4 × 106 m, g = 9.8 m/s2
To find: Gravitational constant (G)
Formula: g = `"GM"/"R"^2`
Calculation: From formula,
G = `"gR"^2/"M"`
G = `(9.8 xx (6.4 xx 10^6)^2)/(6 xx 10^24) = (401.4 xx 10^12)/(6 xx 10^24)`
∴ G = 6.69 × 10-11 Nm2/kg2
The value of gravitational constant is 6.69 × 10-11 Nm2/kg2 .
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?
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.
The time period of an earth-satellite in circular orbit is independent of
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
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T0 and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.
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.
A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth's surface. Find (a) its speed in the orbit, (b) is kinetic energy, (c) the potential energy of the earth-satellite system and (d) its time period. Mass of the earth = 6 × 1024kg.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
The radius of a planet is R1 and a satellite revolves round it in a circle of radius R2. The time period of revolution is T. Find the acceleration due to the gravitation of the planet at its surface.
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 in detail.
State any four applications of a communication satellite.
Answer the following question in detail.
Why an astronaut in an orbiting satellite has a feeling of weightlessness?
Answer the following question in detail.
What is a critical velocity?
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.
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]
There is no atmosphere on moon because ____________.
What is the minimum energy required to launch a satellite of mass 'm' from the surface of the earth of mass 'M' and radius 'R' at an altitude 2R?
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 ______.
Two satellites of masses m and 4m orbit the earth in circular orbits of radii 8r and r respectively. The ratio of their orbital speeds 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 ____________.
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 is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
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 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)
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 an example of a communication (geostationary) satellite launched by India?
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)
