A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero?

Given, the mass of the sun = 2×1030 kg, the mass of the earth =  6×1024kg, and orbital radius = 1.5×1011 m. Neglect the effect of other planets etc.
1. 2.59 × 108 m
2. 3.10 × 108 m
3. 4.07 × 108 m
4. 2.23 × 108 m

Subtopic:  Gravitational Field |
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If the mean orbital radius of the earth around the sun is 1.5×108 km. 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 |
 60%
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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 1.5×108 km 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 |
 54%
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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 |
 73%
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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 |
 83%
From NCERT
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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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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 |
 51%
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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 = 6.0×1024 kg, radius of the earth = 6.4 × 106 m, G = 6.67 × 10-11 N m2 kg-2)

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 |
 50%
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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 = 2×1030 kg; mass of mars = 6.4×1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28×108 km; = 6.67×10-11N m2 kg-2.)
1. 11 × 1010 J
2. 6 × 1011 J
3. 6.67 × 1010 J
4. 7.12 × 1011 J

Subtopic:  Gravitational Potential Energy |
 51%
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