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Q. No.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 |
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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%
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If the escape velocity from a planet's surface is \(v_{\text{esc}}\) and its radius \(R,\) then the gravitational acceleration on its surface equals:
| 1. | \(\dfrac{v^2_{\text{esc}}}{R}\) | 2. | \(\dfrac{v^2_{\text{esc}}}{2R}\) |
| 3. | \(\dfrac{v^2_{\text{esc}}}{2\pi R}\) | 4. | \(\dfrac{2\pi v^2_{\text{esc}}}{R}\) |
Subtopic: Â Escape velocity |
 79%
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The escape velocity of a particle, projected tangentially from the surface of a planet of radius \(R,\) is: (\(g\) is the gravitational acceleration on the planet's surface)
| 1. | \(\sqrt{5gR}\) | 2. | \(\sqrt{3gR}\) |
| 3. | \(\sqrt{2gR}\) | 4. | infinite |
Subtopic: Â Escape velocity |
 80%
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A planet of uniform density has a narrow frictionless tunnel \((AB)\) along its diameter (\(2R\)). The acceleration due to 'gravity' on the surface of the planet is \(g.\)
A particle is given a velocity \(v_e\) and launched radially outward from the mouth of the tunnel. What is the minimum value of \(v_e\) for which the particle escapes the gravitational field?
A particle is given a velocity \(v_e\) and launched radially outward from the mouth of the tunnel. What is the minimum value of \(v_e\) for which the particle escapes the gravitational field?
| 1. | \(\sqrt{gR}\) | 2. | \(\sqrt{2gR}\) |
| 3. | \(\sqrt{\dfrac{gR}{2}}\) | 4. | \(2\sqrt{gR}\) |
Subtopic: Â Escape velocity |
 81%
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A planet of uniform density has a narrow frictionless tunnel \((AB)\) along its diameter (\(2R\)). The acceleration due to 'gravity' on the surface of the planet is \(g.\)
A particle is projected from the centre of the tunnel (centre \(O\) of the planet) with a speed \(u,\) so that it travels along the tunnel and exits; thereafter it escapes the gravity of the planet. The speed of the particle is:
A particle is projected from the centre of the tunnel (centre \(O\) of the planet) with a speed \(u,\) so that it travels along the tunnel and exits; thereafter it escapes the gravity of the planet. The speed of the particle is:
| 1. | \(\sqrt{gR}\) | 2. | \(\sqrt{2gR}\) |
| 3. | \(\sqrt{3gR}\) | 4. | \(\sqrt{5gR}\) |
Subtopic: Â Escape velocity |
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