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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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A point particle of mass \(m\) is placed at the centre \((O)\) of a uniform hemispherical shell of equal mass \(m,\) as shown. A third particle of mass \(m\) is placed at \(A,\) which is at a distance \(2R\) from \(O.\) \(OA\) lies along a diameter of the rim of the hemisphere; \(R\) is its radius. The gravitational potential energy of interaction between \(m~(A)\) and \(m~(O)\) is \(U_1;\) between \(m~(A)\) and \(m\) (hemisphere) is \(U_2\) and; between \(m~(O)\) and \(m\) (hemisphere) is \(U_3.\) Which, of the following, is true?
1. \(|U_1|=|U_2|=|U_3|\)
2. \(|U_2|<|U_1|<|U_3|\)
3. \(|U_1|=|U_2|<|U_3|\)
4. \(|U_3|<|U_1|<|U_2|\)
1. \(|U_1|=|U_2|=|U_3|\)
2. \(|U_2|<|U_1|<|U_3|\)
3. \(|U_1|=|U_2|<|U_3|\)
4. \(|U_3|<|U_1|<|U_2|\)
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%
Hints
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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