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Q. No.What is the ratio of acceleration due to gravity at an altitude \(h=R\) to the value at the surface of the earth? (where \(𝑅\)=radius of earth)
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:6\)
Subtopic: Acceleration due to Gravity |
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If the weight of an object at the Earth’s surface is \(18\) N, what will be its weight when taken to a height of \(3200\) km above the surface? (given: radius of Earth \(=6400\) km)
1. \(9\) N
2. \(8\) N
3. \(20\) N
4. \(18\) N
Subtopic: Acceleration due to Gravity |
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Planet \(A\) has a density and radius represented by \(\rho\) and \(R\) respectively, while planet \(B\) has a density of \(\rho/2\) and a radius of \(1.5R.\) If \(g_{\Large_{AS}}\) and \(g_{\Large_{BS}}\) denote the acceleration at the surface of planets \(A\) and \(B\) respectively, then the ratio \(\dfrac{g_{\Large_{BS}}}{g_{\Large_{AS}}}=\)
1. \(\dfrac{3}{2}\)
2. \(\dfrac{3}{4}\)
3. \(\dfrac{1}{4}\)
4. \(3\)
1. \(\dfrac{3}{2}\)
2. \(\dfrac{3}{4}\)
3. \(\dfrac{1}{4}\)
4. \(3\)
Subtopic: Acceleration due to Gravity |
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The weight of an object on the earth’s surface is \(400\) N. What would be the weight of the same object at a depth \(\dfrac{R}{2}\) from the surface?
(where \(R\) is the radius of the earth)
(where \(R\) is the radius of the earth)
| 1. | \(100\) N | 2. | \(300\) N |
| 3. | \(200\) N | 4. | \(250\) N |
Subtopic: Acceleration due to Gravity |
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Given below are two statements:
| Statement I: | If total energy of a satellite revolving around earth in circular path is \(E\), then potential energy of satellite is \(2E.\) |
| Statement II: | Kinetic energy is also twice of total energy. |
| 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: Satellite |
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If \(W\) is the weight on the surface of the Earth, then the weight of the same body at a height of \(\dfrac{R_e}{4}\) above the surface of Earth is equal to: (\(R_e=\) radius of Earth)
| 1. | \(\dfrac{4}{5}W\) | 2. | \(\dfrac{16}{25}W\) |
| 3. | \(\dfrac{25}{16}W\) | 4. | \(\dfrac{5}{4}W\) |
Subtopic: Acceleration due to Gravity |
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A particle is released from a height equal to radius of earth, \(R.\) Its velocity when it strikes the ground is:
1. \(\sqrt{gR}\)
2. \(\sqrt{{{gR}\over{2}}}\)
3. \(\sqrt{2gR}\)
4. \(\sqrt{4gR}\)
1. \(\sqrt{gR}\)
2. \(\sqrt{{{gR}\over{2}}}\)
3. \(\sqrt{2gR}\)
4. \(\sqrt{4gR}\)
Subtopic: Gravitational Potential Energy |
Level 3: 35%-60%
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Consider the following statements:
Choose the incorrect statement from the given ones:
1. (A) only
2. (B) only
3. (C) only
4. (D) only
| (A) | Planets revolve around the Sun with constant linear speed. |
| (B) | The energy of a planet in an elliptical orbit is constant. |
| (C) | A satellite in circular motion has constant energy. |
| (D) | A body falling towards the Earth results in negligible displacement of the Earth. |
1. (A) only
2. (B) only
3. (C) only
4. (D) only
Subtopic: Kepler's Laws |
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Which of the following expressions gives the value of acceleration due to gravity \((g')\) at the altitude \(h\) above the surface of the Earth?
(\(R:\) radius of Earth; \(g:\) acceleration due to gravity at the surface of Earth)
1. \(g^{\prime}=g \dfrac{h^2}{R^2} \)
2. \(g^{\prime}=\dfrac{g R^2}{(R+h)^2} \)
3. \(g^{\prime}=g\left(1-\dfrac{h}{R}\right) \)
4. \(g^{\prime}=g\left(1-\dfrac{h^2}{R^2}\right)\)
(\(R:\) radius of Earth; \(g:\) acceleration due to gravity at the surface of Earth)
1. \(g^{\prime}=g \dfrac{h^2}{R^2} \)
2. \(g^{\prime}=\dfrac{g R^2}{(R+h)^2} \)
3. \(g^{\prime}=g\left(1-\dfrac{h}{R}\right) \)
4. \(g^{\prime}=g\left(1-\dfrac{h^2}{R^2}\right)\)
Subtopic: Acceleration due to Gravity |
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Two identical particles each of mass m, move in circular path due to their own mutual gravitational force. Find the velocity of the particle if the radius of circular path is a
1. \(\sqrt{{{4Gm}\over{a}}}\)
2. \(\sqrt{{{Gm}\over{2a}}}\)
3. \(\sqrt{{{2Gm}\over{a}}}\)
4. \(\sqrt{{{Gm}\over{4a}}}\)
1. \(\sqrt{{{4Gm}\over{a}}}\)
2. \(\sqrt{{{Gm}\over{2a}}}\)
3. \(\sqrt{{{2Gm}\over{a}}}\)
4. \(\sqrt{{{Gm}\over{4a}}}\)
Subtopic: Newton's Law of Gravitation |
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