The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow: 

1. a, d
2. b, d
3.
 c, e
4. d, e

Subtopic:  Gravitational Field |
 66%
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NEET 2023 - Target Batch - Aryan Raj Singh
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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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NEET 2023 - Target Batch - Aryan Raj Singh
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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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NEET 2023 - Target Batch - Aryan Raj Singh
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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 |
 74%
From NCERT
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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 |
From NCERT
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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:  Gravitational Potential Energy | 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 |
 51%
From NCERT
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