Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given: M = 6.4 × 1023 kg, R = 3.4 × 103 km = 3.4 × 106 m,
To find: Acceleration due to gravity on the surface of the Mars (gM)
Formula: g = `"GM"/"R"^2`
Calculation: As, G = 6.67 × 10-11 Nm2/kg2
From formula,
`"g"_"M" = (6.67 xx 10^-11 xx 6.4 xx 10^23)/(3.4 xx 10^6)^2 = (6.67 xx 6.4)/(3.4 xx 3.4)`
= antilog{log(6.67) + log(6.4) - log(3.4) - log(3.4)}
= antilog{(0.8241) + (0.8062) - (0.5315) - (0.5315)}
= antilog {0.5673}
= 3.693 m/s2
Acceleration due to gravity on the surface of Mars is 3.693 m/s2.
APPEARS IN
RELATED QUESTIONS
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
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 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.
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?
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
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 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 ______
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
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' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity 'ω'. The angular momentum of the satellite is ______.
(G =gravitational constant)
A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.
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.
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 ______.
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)
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 ______.
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)
