Choose the correct alternative.

 1 If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic energy. 2 If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its potential energy. 3 The energy required to launch an orbiting satellite out of earth’s gravitational influence is more than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence. 4 Both (1) and (3) are correct.

Subtopic:  Gravitational Potential Energy |
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A rocket is fired vertically with a speed of $$5$$ km/s from the earth’s surface. How far from the earth does the rocket go before returning to the earth?
1. $$8\times10^6$$ m
2. $$1.6\times10^6$$ m
3. $$6.4\times10^6$$ m
4. $$12\times10^6$$ m

Subtopic:  Gravitational Potential Energy |
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A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? (Mass of the space ship = 1000 kg; mass of the sun = 2×${10}^{30}$ kg; mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28×${10}^{8}$ km; = 6.67×${10}^{-11}$.)
1. 11 × 1010 J
2. 6 × 1011 J
3. 6.67 × 1010 J
4. 7.12 × 1011 J

Subtopic:  Gravitational Potential Energy |
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A rocket is fired vertically from the surface of mars with a speed of 2 km/s. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it?

(Mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; G = 6.67×${10}^{-11}$ )

1. 477.2 km
2. 550.5 km
3. 493.9 km
4. 517.3 km

Subtopic:  Gravitational Potential Energy |
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