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Q. No.A particle of mass \(m\) is projected with a velocity, \(v=kv_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is:
(Where \(v_e=\) escape velocity, \(R=\) the radius of the earth)
1.
\(\dfrac{R^{2}k}{1+k}\)
2.
\(\dfrac{Rk^{2}}{1-k^{2}}\)
3.
\(R\left ( \dfrac{k}{1-k} \right )^{2}\)
4.
\(R\left ( \dfrac{k}{1+k} \right )^{2}\)
(Where \(v_e=\) escape velocity, \(R=\) the radius of the earth)
Subtopic: Escape velocity |
62%
Level 2: 60%+
NEET - 2021
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The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is:
| 1. | \(3v\) | 2. | \(4v\) |
| 3. | \(v\) | 4. | \(2v\) |
Subtopic: Escape velocity |
62%
Level 2: 60%+
NEET - 2021
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A particle is released from a height of \(S\) above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The distance from the earth's surface and the speed of the particle at that instant are respectively:
| 1. | \(\frac{S}{2},\frac{\sqrt{3gS}}{2}\) | 2. | \(\frac{S}{4}, \sqrt{\frac{3gS}{2}}\) |
| 3. | \(\frac{S}{4},\frac{3gS}{2}\) | 4. | \(\frac{S}{4},\frac{\sqrt{3gS}}{3}\) |
Subtopic: Gravitational Potential Energy |
70%
Level 2: 60%+
NEET - 2021
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Assume that earth and mars move in circular orbits around the sun, with the martian orbit being \(1.52\) times the orbital radius of the earth. The length of the martian year in days is approximately:
(Take \((1.52)^{3/2}=1.87\))
| 1. | \(344\) days | 2. | \(684\) days |
| 3. | \(584\) days | 4. | \(484\) days |
Subtopic: Kepler's Laws |
67%
Level 2: 60%+
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A \(400~\text{kg}\) satellite is in a circular orbit of radius \(2R_E\) about the Earth. What are the changes in the kinetic and potential energies respectively to transfer it to a circular orbit of radius \(4R_{E}.\) (where \(R_E\) is the radius of the Earth)
1. \(3.13\times 10^{9}~\text{J}~\text{and}~6.25\times10^{9}~\text{J}\)
2. \(3.13\times 10^{9}~\text{J}~\text{and}~-6.25\times10^{9}~\text{J}\)
3. \(-3.13\times 10^{9}~\text{J}~\text{and}~-6.25\times10^{9}~\text{J}\)
4. \(-3.13\times 10^{8}~\text{J}~\text{and}~-6.25\times10^{8}~\text{J}\)
1. \(3.13\times 10^{9}~\text{J}~\text{and}~6.25\times10^{9}~\text{J}\)
2. \(3.13\times 10^{9}~\text{J}~\text{and}~-6.25\times10^{9}~\text{J}\)
3. \(-3.13\times 10^{9}~\text{J}~\text{and}~-6.25\times10^{9}~\text{J}\)
4. \(-3.13\times 10^{8}~\text{J}~\text{and}~-6.25\times10^{8}~\text{J}\)
Subtopic: Satellite |
Level 4: Below 35%
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A \(400~\text{kg}\) satellite is in a circular orbit of radius \(2R_E\) (where \(R_E\) is the radius of the earth) about the Earth. How much energy is required to transfer it to a circular orbit of radius \(4R_E ~?\)
(given: \(R_E=6.4\times10^{6}~\text{m}\) )
(given: \(R_E=6.4\times10^{6}~\text{m}\) )
| 1. | \(3.13\times10^{9}~\text{J}\) | 2. | \(3.13\times10^{10}~\text{J}\) |
| 3. | \(4.13\times10^{9}~\text{J}\) | 4. | \(4.13\times10^{8}~\text{J}\) |
Subtopic: Satellite |
59%
Level 3: 35%-60%
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The moon is at a distance of \(3.84\times10^5~\text{km}\) from the earth. Its time period of revolution in days is:
\(\left(\text{Given: }k=\dfrac{4\pi^2}{GM_E}=1.33\times10^{-14}~\text{days}^{2}\text-\text{km}^{-3}\right)\)
1. \(17.3\) days
2. \(33.7\) days
3. \(27.3\) days
4. \(4\) days
\(\left(\text{Given: }k=\dfrac{4\pi^2}{GM_E}=1.33\times10^{-14}~\text{days}^{2}\text-\text{km}^{-3}\right)\)
1. \(17.3\) days
2. \(33.7\) days
3. \(27.3\) days
4. \(4\) days
Subtopic: Satellite |
66%
Level 2: 60%+
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Constant \(k = 10^{- 13} ~ \text s^{2}~ \text m^{- 3}\) in days and kilometres is?
1. \(10^{- 13} ~ \text d^{2} ~\text{km}^{- 3}\)
2. \(1 . 33 \times 10^{14} \text{ dkm}^{- 3}\)
3. \(10^{- 13} ~ \text d^{2} ~\text {km}\)
4. \(1 . 33 \times 10^{- 14} \text{ d}^{2} \text{ km}^{- 3}\)
1. \(10^{- 13} ~ \text d^{2} ~\text{km}^{- 3}\)
2. \(1 . 33 \times 10^{14} \text{ dkm}^{- 3}\)
3. \(10^{- 13} ~ \text d^{2} ~\text {km}\)
4. \(1 . 33 \times 10^{- 14} \text{ d}^{2} \text{ km}^{- 3}\)
Subtopic: Satellite |
57%
Level 3: 35%-60%
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You are given the following data: \(g = 9.81~\text{m/s}^{2}\), \(R_{E} = 6 . 37 \times 10^{6}~\text m\), the distance to the moon, \(R = 3 . 84 \times 10^{8}~\text m\) and the time period of the moon’s revolution is \(27.3\) days. Mass of the Earth \(M_{E}\) in two different ways is:
1. \(5 . 97 \times 10^{24} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
2. \(5 . 97 \times 10^{24} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
3. \(5 . 97 \times 10^{23} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
4. \(5 . 97 \times 10^{23} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
1. \(5 . 97 \times 10^{24} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
2. \(5 . 97 \times 10^{24} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
3. \(5 . 97 \times 10^{23} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
4. \(5 . 97 \times 10^{23} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
Subtopic: Satellite |
56%
Level 3: 35%-60%
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The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of \(9 . 4 \times 10^{3}\) km. The mass of mars is:
| 1. | \(6 . 48 \times 10^{23} \text{ kg}\) | 2. | \(6 . 48 \times 10^{25} \text{ kg}\) |
| 3. | \(6 . 48 \times 10^{20} \text{ kg}\) | 4. | \(6 . 48 \times 10^{21} \text{ kg}\) |
Subtopic: Satellite |
Level 3: 35%-60%
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