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 nut becomes loose and gets detached from a satellite revolving around the earth. Will it land on the earth? If yes, where will it land? If no, how can an astronaut make it land on the earth?
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?
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?
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
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 ______.
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
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 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]
Which of the following statements is CORRECT in respect of a geostationary satellite?
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 ______.
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
The period of revolution of a satellite 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.
The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).
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)
What is the typical altitude range for a polar satellite's orbit?
Which of the following is an example of a communication (geostationary) satellite launched by India?
Artificial satellites are launched for all the following purposes EXCEPT:
Which of the following is the only natural satellite of the Earth?
