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Q. No.If a body of mass \(m\) placed on the earth's surface is taken to a height of \(h = 3R,\) then the change in gravitational potential energy is:
1. \(\dfrac{mgR}{4}\)
2. \(\dfrac{2}{3} mgR\)
3. \(\dfrac{3}{4} mgR\)
4. \(\dfrac{mgR}{2}\)
Subtopic: Gravitational Potential Energy |
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Level 1: 80%+
AIPMT - 2002
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How much work per kilogram needs to be done to shift a \(1\) kg mass from the surface of the earth to infinity? (Take acceleration due to gravity \(=g\) and radius of the earth \(=R\).)
| 1. | \(\dfrac{g}{R}\) | 2. | \(\dfrac{R}{g}\) |
| 3. | \(gR\) | 4. | \(\dfrac{g}{R^{2}}\) |
Subtopic: Gravitational Potential Energy |
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Level 1: 80%+
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A body of mass \(m\) is taken from the earth's surface to the height \(h\) equal to the radius of the earth, the increase in potential energy will be:
1. \(mgR\)
2. \(\dfrac{1}{2}mgR\)
3. \(2 ~mgR\)
4. \(\dfrac{1}{4}~mgR\)
Subtopic: Gravitational Potential Energy |
82%
Level 1: 80%+
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If three particles each of mass \(M\) are placed at the corners of an equilateral triangle of side \(a,\) the potential energy of the system and the work done if the side of the triangle is changed from \(a\) to \(2a,\) are:
1. \(\dfrac{3GM}{{a}^{2}},\dfrac{3GM}{2a}\)
2. \({-}\dfrac{3{GM}^{2}}{{a}}{,}\dfrac{3{GM}^{2}}{2a}\)
3. \({-}\dfrac{3{GM}^{2}}{{a}^{2}}{,}\dfrac{3{GM}^{2}}{4{a}^{2}}\)
4. \({-}\dfrac{3{GM}^{2}}{a}{,}\dfrac{3GM}{2a}\)
1. \(\dfrac{3GM}{{a}^{2}},\dfrac{3GM}{2a}\)
2. \({-}\dfrac{3{GM}^{2}}{{a}}{,}\dfrac{3{GM}^{2}}{2a}\)
3. \({-}\dfrac{3{GM}^{2}}{{a}^{2}}{,}\dfrac{3{GM}^{2}}{4{a}^{2}}\)
4. \({-}\dfrac{3{GM}^{2}}{a}{,}\dfrac{3GM}{2a}\)
Subtopic: Gravitational Potential Energy |
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Level 2: 60%+
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In the gravitational field of the Earth (mass \(M\)), a point mass \(m\) is located at a distance \(r\) from Earth's centre. Which of the following expressions correctly represents the gravitational potential energy of the system, given that \(G\) is the universal gravitational constant and the zero of potential energy is taken at infinity?
| 1. | \(\dfrac{GMm}{r}\) | 2. | \(\dfrac{-GMm}{r}\) |
| 3. | \(\dfrac{GM}{r}\) | 4. | \(\dfrac{-GM}{r}\) |
Subtopic: Gravitational Potential Energy |
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Match the following physical quantities related to the Earth–Sun system:
(Given: Mass of sun = \(M_s,\) Mass of earth =\(M_e,\) Radius of earth = \(R,\) Distance between sun and earth =\(a\))
Codes:
(Given: Mass of sun = \(M_s,\) Mass of earth =\(M_e,\) Radius of earth = \(R,\) Distance between sun and earth =\(a\))
| \(\mathrm{(A)}\) | The kinetic energy of the earth | \(\mathrm{(I)}\) | \(-\dfrac{G M_s M_e}{a}\) |
| \(\mathrm{(B)}\) | The potential energy of the earth and the sun | \(\mathrm{(II)}\) | \(\dfrac{G M_s M_e}{2 a}\) |
| \(\mathrm{(C)}\) | The total energy of the earth and the sun | \(\mathrm{(III)}\) | \(\dfrac{G M_e}{R}\) |
| \(\mathrm{(D)}\) | Escape energy from the surface of the earth per unit mass | \(\mathrm{(IV)}\) | \(-\dfrac{G M_s M_e}{2 a}\) |
Codes:
| 1. | \(\mathrm{A\text-II,B\text-I,C\text- IV,D\text- III}\) |
| 2. | \(\mathrm{A\text-I,B\text-II,C\text- III,D\text- IV}\) |
| 3. | \(\mathrm{A\text-III,B\text-IV,C\text- I,D\text- II}\) |
| 4. | \(\mathrm{A\text-IV,B\text-III,C\text- II,D\text- I}\) |
Subtopic: Gravitational Potential Energy |
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Level 2: 60%+
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