Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
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
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
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.
(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.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
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 ______.
Answer the following question.
Define the binding energy of a satellite.
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Derive an expression for the critical velocity of a satellite.
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
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
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?
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 ______.
Two satellites of masses m1 and m2 (m1 > m2) are revolving round the earth in circular orbit of radii r1 and r2 (r1 > r2) respectively. Which of the following statements is true regarding their speeds v1 and v2?
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 ____________.
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 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?
Two satellites are orbiting around the earth in circular orbits of same radius. One of them is 10 times greater in mass than the other. Their period of revolutions are in the ratio ______.
