Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?
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
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
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) 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.
What do you mean by geostationary satellite?
Answer the following question.
What is periodic time of a geostationary satellite?
Answer the following question in detail.
State any four applications of a communication satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth.
Given: G = 6.67 × 10-11 Nm2/kg2
R = 6400 km, M = 6 × 1024 kg
Answer the following question in detail.
Two satellites A and B are revolving round a planet. Their periods of revolution are 1 hour and 8 hour respectively. The radius of orbit of satellite B is 4 × 104 km. Find radius of orbit of satellite A.
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)
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.
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 ______
There is no atmosphere on moon because ____________.
Reason of weightlessness in a satellite 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 ____________.
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 ____________.
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?
A satellite is to revolve round the earth in a circle of radius 9600 km. The speed with which this satellite be projected into an orbit, will be ______.
The period of revolution of a satellite is ______.
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
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)
