- 1(current)
Q. No.
| 1. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |
| 3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |
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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. | \(g_s\sqrt{\dfrac{2}{k}} \) |
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| 1. | \(\dfrac{v^2_{\text{esc}}}{R}\) | 2. | \(\dfrac{v^2_{\text{esc}}}{2R}\) |
| 3. | \(\dfrac{v^2_{\text{esc}}}{2\pi R}\) | 4. | \(\dfrac{2\pi v^2_{\text{esc}}}{R}\) |
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| 1. | \(\sqrt{5gR}\) | 2. | \(\sqrt{3gR}\) |
| 3. | \(\sqrt{2gR}\) | 4. | infinite |
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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. | \(2\sqrt{gR}\) |
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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. | \(\sqrt{5gR}\) |
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- 1(current)
Q. No.
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