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Q. No.Two planets orbit a star in circular paths with radii \(R\) and \(4R,\) respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is \(T,\) what is the minimum time after which the star and the planets will again be aligned in a straight line?
1.
\((4)^2T\)
2.
\((4)^{\frac13}T\)
3.
\(2T\)
4.
\(8T\)
Subtopic: Kepler's Laws |
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NEET - 2022
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In a gravitational field, the gravitational potential is given by; \(V=-\frac{K}{x}~\text{J/kg}.\) The gravitational field intensity at the point \((2,0,3)~\text m\) is:
| 1. | \(+\dfrac K2\) | 2. | \(-\dfrac{K}{2}\) |
| 3. | \(-\dfrac{K}{4}\) | 4. | \(+\dfrac K4\)
|
Subtopic: Gravitational Field |
From NCERT
NEET - 2022
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Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:
| 1. | increases with increasing altitude. |
| 2. | increases with increasing depth. |
| 3. | is independent of the mass of the earth. |
| 4. | is independent of the mass of the body. |
Subtopic: Acceleration due to Gravity |
70%
From NCERT
NEET - 2022
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II | ||
| (a) | Gravitational constant (\(G\)) | (i) | \([{L}^2 {~T}^{-2}] \) |
| (b) | Gravitational potential energy | (ii) | \([{M}^{-1} {~L}^3 {~T}^{-2}] \) |
| (c) | Gravitational potential | (iii) | \([{LT}^{-2}] \) |
| (d) | Gravitational intensity | (iv) | \([{ML}^2 {~T}^{-2}]\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (i) | (iii) |
| 2. | (ii) | (i) | (iv) | (iii) |
| 3. | (ii) | (iv) | (i) | (iii) |
| 4. | (ii) | (iv) | (iii) | (i) |
Subtopic: Gravitational Potential |
71%
From NCERT
NEET - 2022
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A body of mass \(60~ \text{g}\) experiences a gravitational force of \(3.0~\text{N}\) when placed at a particular point. The magnitude of the gravitational field intensity at that point is:
| 1. | \(180 ~\text{N/kg}\) | 2. | \(0.05 ~\text{N/kg}\) |
| 3. | \(50 ~\text{N/kg}\) | 4. | \(20 ~\text{N/kg}\) |
Subtopic: Gravitational Field |
72%
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NEET - 2022
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A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2 a. The gravitational field at a distance \(\frac{3}{2} a\) from the center is:
1. \(\frac{4 G M}{3 a^{2}}\)
2. \(\frac{8 G M}{25 a^{2}}\)
3. \(\frac{ G M}{ a^{2}}\)
4. \(\frac{4 G M}{9 a^{2}}\)
1. \(\frac{4 G M}{3 a^{2}}\)
2. \(\frac{8 G M}{25 a^{2}}\)
3. \(\frac{ G M}{ a^{2}}\)
4. \(\frac{4 G M}{9 a^{2}}\)
Subtopic: Gravitational Field |
66%
From NCERT
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A satellite is revolving around the earth at a height of 600 km. The radius of the earth = 6400 km and mass of the earth = \(=6 \times 10^{24} \mathrm{~kg}\). The speed of the satellite is given by:
1. \(76 \mathrm{~km} \mathrm{~s}^{-1}\)
2. \(7.6 \mathrm{~km} \mathrm{~s}^{-1}\)
3. \(4.2 \mathrm{~km} \mathrm{~s}^{-1}\)
4. \(42 \mathrm{~km} \mathrm{~s}^{-1}\)
1. \(76 \mathrm{~km} \mathrm{~s}^{-1}\)
2. \(7.6 \mathrm{~km} \mathrm{~s}^{-1}\)
3. \(4.2 \mathrm{~km} \mathrm{~s}^{-1}\)
4. \(42 \mathrm{~km} \mathrm{~s}^{-1}\)
Subtopic: Orbital velocity |
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Two bodies of mass \(m\) and \(9m\) are placed at a distance \(R.\) The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be:
(\(G=\) gravitational constant)
1. \(-\dfrac{20~Gm}{R}\)
2. \(-\dfrac{8~Gm}{R}\)
3. \(-\dfrac{12~Gm}{R}\)
4. \(-\dfrac{16~Gm}{R}\)
(\(G=\) gravitational constant)
1. \(-\dfrac{20~Gm}{R}\)
2. \(-\dfrac{8~Gm}{R}\)
3. \(-\dfrac{12~Gm}{R}\)
4. \(-\dfrac{16~Gm}{R}\)
Subtopic: Gravitational Potential |
54%
From NCERT
NEET - 2023
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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 |
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From NCERT
NEET - 2023
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The escape velocity of a body on the earth's surface is \(11.2~\text{km/s}.\) If the same body is projected upward with a velocity \(22.4~\text{km/s},\) the velocity of this body at an infinite distance from the centre of the earth will be:
| 1. | \(11.2\sqrt2~\text{km/s}\) | 2. | zero |
| 3. | \(11.2~\text{km/s}\) | 4. | \(11.2\sqrt3~\text{km/s}\) |
Subtopic: Escape velocity |
From NCERT
NEET - 2023
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