# The escape speed of a projectile on the earth’s surface is $$11.2$$ km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth?  (Ignore the presence of the sun and other planets.) 1. $$32.7$$ km/s 2. $$11.2$$ km/s 3. $$31.7$$ km/s 4. $$21.2$$ km/s

Subtopic:  Escape velocity |
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A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? (Mass of the satellite = 200 kg; mass of the earth = 6.0×${10}^{24}$ kg, radius of the earth = 6.4 × ${10}^{6}$ m, G = 6.67 × ${10}^{-11}$ )

1. 7.5 × 109 J
2. 4.7 × 109 J
3. 4.4 × 109 J
4. 5.9 × 109 J

Subtopic:  Satellite |
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Two heavy spheres each of mass $$100$$ kg and radius $$0.10$$ m are placed $$1.0$$ m apart on a horizontal table. What is the gravitational potential at the midpoint of the line joining the centres of the spheres?

 1 $$2.67\times10^{-8}$$ J kg–1 2 $$0$$ 3 $$6.67\times10^{-9}$$ J kg–1 4 $$3.71\times10^{-8}$$ J kg–1
Subtopic:  Gravitational Potential |
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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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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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Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed $$250$$ N on the surface?

 1 $$250$$ N 2 $$125$$ N 3 $$175$$ N 4 $$145$$ N
Subtopic:  Acceleration due to Gravity |
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A body weighs $$63$$ N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?
1. $$98$$ N
2. $$35$$ N
3. $$63$$ N
4. $$28$$ N

Subtopic:  Acceleration due to Gravity |
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A Saturn year is 29.5 times the earth year. How far is Saturn from the sun if the earth is  away from the sun?
1. 2.01 × 1012 m
2. 3.86 × 1012 m
3. 1.43 × 1012 m
4. 4.19 × 1012 m

Subtopic:  Kepler's Laws |
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If the mean orbital radius of the earth around the sun is . Then the mass of the sun is approximately:
1. 3 × 1034 kg
2. 2 × 1030 kg
3. 1.5 × 1028 kg
4. 1.0 × 1035 kg

Subtopic:  Newton's Law of Gravitation |
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