Q. No.A satellite is orbiting just above the surface of the earth with period \(T.\) If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\frac{3 \pi}{G d}\) represents:
1. \(\sqrt{T}\)
2. \(T\)
3. \(T^2\)
4. \(T^3\)
1. \(\sqrt{T}\)
2. \(T\)
3. \(T^2\)
4. \(T^3\)
Subtopic: Satellite |
70%
From NCERT
NEET - 2023
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A satellite of mass \(M\) is revolving around the Earth in a stationary orbit with a time period \(T.\) If \(10\%\) of the satellite's mass is detached, what will happen to its time period?
1. remain the same
2. increase by \(10\%\)
3. decrease by \(10\%\)
4. decrease by \(20\%\)
Subtopic: Satellite |
81%
From NCERT
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The minimum energy required to launch a satellite of mass \(m\) from the surface of the earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\) from the surface of the earth is:
| 1. | \(\frac{2 G m M}{3 R} \) | 2. | \(\frac{G m M}{2 R} \) |
| 3. | \(\frac{G m M}{3 R} \) | 4. | \( \frac{5 G m M}{6 R}\) |
Subtopic: Satellite |
From NCERT
NEET - 2024
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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 |
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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 |
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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 |
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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 |
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From NCERT
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A planet is orbiting the sun in an elliptical orbit. Let \(U\) denote the potential energy and \(K\) denote the kinetic energy of the planet at an arbitrary point in the orbit.
Choose the correct statement from the given ones:
| 1. | \(K<\left| U\right|\) always |
| 2. | \(K>\left| U\right|\) always |
| 3. | \(K=\left| U\right|\) always |
| 4. | \(K=\left| U\right|\) for two positions of the planet in the orbit |
Subtopic: Satellite |
60%
From NCERT
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Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because:
| 1. | the solar cells and batteries in satellites run out. |
| 2. | the laws of gravitation predict a trajectory spiralling inwards. |
| 3. | of viscous forces causing the speed of the satellite and hence height to gradually decrease. |
| 4. | of collisions with other satellites. |
Subtopic: Satellite |
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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 |
58%
From NCERT
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