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A satellite is in a circular orbit around a planet, orbiting with a speed of \(2\) km/s. What is the minimum additional velocity that should be given to it, perpendicular to its motion, so that it escapes?
| 1. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |
| 3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |
Subtopic: Â Escape velocity |
Level 4: Below 35%
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Two large uniform solid spheres each of mass \(M,\) radius \(R\) are in contact with each other. If a particle is launched from a point on the surface of a sphere, diametrically opposite to the contact point, its escape velocity will be:
1. \(\sqrt{\dfrac{4GM}{R}}\)
2. \(\sqrt{\dfrac{4GM}{3R}}\)
3. \(\sqrt{\dfrac{8GM}{3R}}\)
4. \(\sqrt{\dfrac{2GM}{3R}}\)
1. \(\sqrt{\dfrac{4GM}{R}}\)
2. \(\sqrt{\dfrac{4GM}{3R}}\)
3. \(\sqrt{\dfrac{8GM}{3R}}\)
4. \(\sqrt{\dfrac{2GM}{3R}}\)
Subtopic: Â Escape velocity |
Level 3: 35%-60%
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The acceleration due to gravity, \(g\), near a spherically symmetric planet's surface decreases with height, \(h\) according to the relation:
\(g(h)= g_s-k\cdot h\), where \(h\ll\) the radius of the planet.
The escape speed from the planet's surface is:
| 1. | \(\dfrac{g_s}{2\sqrt k}\) | 2. | \(\dfrac{g_s}{\sqrt k}\) |
| 3. | \(\dfrac{2g_s}{\sqrt k}\) | 4. | \(g_s\sqrt{\dfrac{2}{k}} \) |
Subtopic: Â Escape velocity |
 54%
Level 3: 35%-60%
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