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Q. No.The angular momentum of a planet of mass \(m,\) moving around the sun (mass: \(M\gg m\)) in an orbit of radius \(r\) is proportional to:
1.
\(mr\)
2.
\(\dfrac{m}{r}\)
3.
\(m\sqrt r\)
4.
\(\dfrac{m}{\sqrt r}\)
Subtopic: Kepler's Laws |
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Three stars of identical masses \(m\) move around a central star of mass \(M\) in an orbit of radius \(r.\) The net gravitational force acting on any one of the orbiting stars equals:
| 1. | \(\dfrac{GMm}{r^2}+\dfrac{2Gm^2}{r^2}\) |
| 2. | \(\dfrac{GMm}{r^2}+\dfrac{\sqrt3Gm^2}{r^2}\) |
| 3. | \(\dfrac{GMm}{r^2}+\dfrac{Gm^2}{\sqrt3r^2}\) |
| 4. | \(\dfrac{GMm}{r^2}+\dfrac{2Gm^2}{\sqrt3r^2}\) |
Subtopic: Newton's Law of Gravitation |
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A particle of mass \(m\) is placed at the mid-point of the radius of a thin uniform spherical shell of mass \(M,\) as shown in the figure. Consider the plane that slices the shell into two parts: the plane is perpendicular to the radius and passes through \(m.\) The upper part of the shell has a mass \(\dfrac M4\) and the lower part \(\dfrac{3M}{4}.\) Let the gravitational force exerted by the upper part of the shell on the particle be \(F.\) The force exerted by the lower part of the shell on the particle is:
| 1. | \(3F\) | 2. | \(2F\) |
| 3. | \(4F\) | 4. | \(F\) |
Subtopic: Newton's Law of Gravitation |
55%
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A planet moves around the sun in an elliptical orbit with the perihelion at \(P ,\) and aphelion at \(A\). Let the quantities be defined as follows: (for the planet)
The subscripts refer to the quantity measured at the perihelion \((P)\) or aphelion \((A)\): \(v_P\) is the speed at perihelion, \(K_A\) is the kinetic energy at aphelion, etc. Then,
1. \(K_A r^2_A = K_Pr^2_P\)
2. \(v_A r_A = v_P~r_P\)
3. \(U_Ar_A = U_P r_P\)
4. All the above are true
| \(r\) | distance from sun \(S\) |
| \(v\) | speed in orbit |
| \(K\) | kinetic energy |
| \(U\) | potential energy |
The subscripts refer to the quantity measured at the perihelion \((P)\) or aphelion \((A)\): \(v_P\) is the speed at perihelion, \(K_A\) is the kinetic energy at aphelion, etc. Then,
1. \(K_A r^2_A = K_Pr^2_P\)
2. \(v_A r_A = v_P~r_P\)
3. \(U_Ar_A = U_P r_P\)
4. All the above are true
Subtopic: Kepler's Laws |
67%
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A satellite is in a circular orbit around a planet, orbiting with a speed of \(2\) km/s. What is the minimum additional velocity that should be given to it, perpendicular to its motion, so that it escapes?
| 1. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |
| 3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |
Subtopic: Escape velocity |
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The force of gravitation between a particle \(A,\) and another particle \(B\) when separated by a distance \(r\) is \(F_{AB};\) while the force between a particle \(C\) and \(A\) separated by the same distance is \(4F_{AB}.\) The ratio of the masses of \(B\) and \(C\) is:
| 1. | \(4\) | 2. | \(2\) |
| 3. | \(\dfrac12\) | 4. | \(\dfrac14\) |
Subtopic: Newton's Law of Gravitation |
81%
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Given below are two statements:
| Statement I: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is between the Earth and the Sun. |
| Statement II: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is opposite to the Sun, relative to the Earth. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Newton's Law of Gravitation |
72%
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Given below are two statements:
| Statement I: | The gravitational force acting on a particle depends on the electric charge of the particle. |
| Statement II: | The gravitational force on an extended body can be calculated by assuming the body to be a particle 'concentrated' at its centre of mass and applying Newton's law of gravitation. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Newton's Law of Gravitation |
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Given below are two statements:
| Statement I: | The kinetic energy of a planet is maximum when it is closest to the sun. |
| Statement II: | The time taken by a planet to move from the closest position (perihelion) to the farthest position (aphelion) is larger for a planet that is farther from the sun. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Kepler's Laws |
70%
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The gravitational potential energy of a particle of mass \(m\) increases by \(mgh,\) when it is raised through a height \(h\) in a uniform gravitational field "\(g\)". If a particle of mass \(m\) is raised through a height \(h\) in the earth's gravitational field (\(g\): the field on the earth's surface) and the increase in gravitational potential energy is \(U\), then:
| 1. | \(U > mgh\) |
| 2. | \(U < mgh\) |
| 3. | \(U = mgh\) |
| 4. | any of the above may be true depending on the value of \(h,\) considered relative to the radius of the earth. |
Subtopic: Gravitational Potential Energy |
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