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Q. No.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 |
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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 |
70%
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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 |
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If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:
| 1. | \(\dfrac{\pi RG}{12g}\) | 2. | \(\dfrac{3\pi R}{4gG}\) |
| 3. | \(\dfrac{3g}{4\pi RG}\) | 4. | \(\dfrac{4\pi G}{3gR}\) |
Subtopic: Acceleration due to Gravity |
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NEET - 2023
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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 |
73%
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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 |
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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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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 |
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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 |
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NEET - 2021
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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. | \(R\left ( \dfrac{k}{1+k} \right )^{2}\) |
Subtopic: Escape velocity |
62%
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