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Q. No.A block of mass \(m\) is slowly taken vertically upward over a large distance \(h\) in the earth's gravitational field, starting from its surface. The gravitational field at its final destination is \({\Large\frac{g}{27}},\) where \(g\) is the field at the earth's surface. The work done in the process is:
| 1. | \(mgh\) | 2. | \(\Large\frac{mgh}{27}\) |
| 3. | \(\Large\frac{mgh}{\sqrt{27}}\) | 4. | \(\Large\frac{14mgh}{27}\) |
Subtopic: Â Gravitational Potential Energy |
Level 3: 35%-60%
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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: Â Gravitational Potential Energy |
Level 3: 35%-60%
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Given below are two statements:
| Assertion (A): | In a system of particles interacting by means of gravitational forces, the gravitational potential energy is a function of the distances between the particles only. |
| Reason (R): | Gravitational force is a conservative force; it depends on the separation between the two interacting particles, and acts along the line joining them. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Gravitational Potential Energy |
Level 3: 35%-60%
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Consider a small body falling freely onto the surface of the earth from a height \(2R\) above its surface (\(R\) being the radius of the earth). Ignore any air resistance. The change in the gravitational potential energy of the body, per unit mass, is: (take the acceleration due to gravity on the surface to be \(g\))
| 1. | \(4gR\) | 2. | \(\Large\frac{4gR}{3}\) |
| 3. | \(\dfrac{2gR}{3}\) | 4. | \(\Large\frac{gR}{3}\) |
Subtopic: Â Gravitational Potential Energy |
 71%
Level 2: 60%+
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A thin uniform shell, of mass \(m\) & radius \(R,\) is floating in outer space, in the absence of any other gravitational fields, except its own. The gravitational acceleration on its outer surface is \(g.\) The gravitational self energy of the sphere is
| 1. | \(-mgR\) | 2. | \(-{\Large\frac12}mgR\) |
| 3. | \(-{\Large\frac35}mgR\) | 4. | \(-2mgR\) |
Subtopic: Â Gravitational Potential Energy |
 75%
Level 2: 60%+
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A small light asteroid moves along the path: \(y=\dfrac{x^2}{4}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The total energy of the asteroid, per unit mass, is:
1. \(1\)
2. \(2\)
3. zero
4. \(\pi^2\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The total energy of the asteroid, per unit mass, is:
1. \(1\)
2. \(2\)
3. zero
4. \(\pi^2\)
Subtopic: Â Gravitational Potential Energy |
 63%
Level 2: 60%+
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A planet of uniform density has a narrow frictionless tunnel \((AB)\) along its diameter (\(2R\)). The acceleration due to 'gravity' on the surface of the planet is \(g.\)
A particle is dropped from \(A\) (the entrance) into the tunnel. What will be its speed when it reaches the centre?
A particle is dropped from \(A\) (the entrance) into the tunnel. What will be its speed when it reaches the centre?
| 1. | \(\sqrt{gR}\) | 2. | \(\sqrt{\dfrac{gR}{2}}\) |
| 3. | \(\sqrt{3gR}\) | 4. | \(\sqrt{2gR}\) |
Subtopic: Â Gravitational Potential Energy |
Level 3: 35%-60%
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