Q. No.The speed of a planet at the perihelion is \(v_p\) and the sun planet distance is \(r_p.\) The corresponding quantities at the aphelion are \(v_a\) and \(r_a\) respectively. Then:
1. \(\dfrac{v_p}{v_a}=\dfrac{r_p}{r_a}\)
2. \(\dfrac{v_p}{v_a}=\dfrac{r_a}{r_p}\)
3. \(\dfrac{v_p}{v_a}=\dfrac{\sqrt{r_p}}{\sqrt{r_a}}\)
4. \(\dfrac{v_p}{v_a}=\dfrac{\sqrt{r_a}}{\sqrt{r_p}}\)
1. \(\dfrac{v_p}{v_a}=\dfrac{r_p}{r_a}\)
2. \(\dfrac{v_p}{v_a}=\dfrac{r_a}{r_p}\)
3. \(\dfrac{v_p}{v_a}=\dfrac{\sqrt{r_p}}{\sqrt{r_a}}\)
4. \(\dfrac{v_p}{v_a}=\dfrac{\sqrt{r_a}}{\sqrt{r_p}}\)
Subtopic: Acceleration due to Gravity |
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If the mass of the sun were ten times smaller and gravitational constant \(G\) were ten times larger in magnitude. Then,
| (a) | walking on the ground would become more difficult. |
| (b) | the acceleration due to gravity on the earth will not change. |
| (c) | raindrops will fall much faster. |
| (d) | aeroplanes will have to travel much faster. |
Choose the correct alternatives:
1. (a), (b), (c)
2. (a), (d)
3. (b), (c), (d)
4. (a), (c), (d)
Subtopic: Acceleration due to Gravity |
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Given below are two statements:
| Statement I: | The value of acceleration due to gravity is same at all the points inside earth assuming it to be made up of uniform density. |
| Statement II: | The value of gravitational field increases as we go towards centre in a uniform spherical shell. |
| 1. | Both Statement I and Statement II are True. |
| 2. | Statement I is True but Statement II is False. |
| 3. | Statement I is False but Statement II is True. |
| 4. | Both Statement I and Statement II are False. |
Subtopic: Acceleration due to Gravity |
55%
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The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity:
| 1. | will be directed towards the centre but not the same everywhere. |
| 2. | will have the same value everywhere but not directed towards the centre. |
| 3. | will be the same everywhere in magnitude directed towards the centre. |
| 4. | cannot be zero at any point. |
Subtopic: Acceleration due to Gravity |
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The value of acceleration due to gravity on the surface of a planet of radius \(0.5\) times earth's radius is \(0.8g.\) The mass of the planet is: (Where \(g=10\) m/s2, \(M_{E}=\) Mass of Earth)
1. \(0.1M_{E}\)
2. \(0.2M_{E}\)
3. \(0.4M_{E}\)
4. \(M_{E}\)
1. \(0.1M_{E}\)
2. \(0.2M_{E}\)
3. \(0.4M_{E}\)
4. \(M_{E}\)
Subtopic: Acceleration due to Gravity |
81%
From NCERT
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Imagine that there exists a planet whose mass and radius are both half that of the earth. The acceleration due to gravity on that planet will be:
1. \(g/4\)
2. \(g/2\)
3. \(2g\)
4. \(4g\)
1. \(g/4\)
2. \(g/2\)
3. \(2g\)
4. \(4g\)
Subtopic: Acceleration due to Gravity |
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Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:
| 1. | increases with increasing altitude. |
| 2. | increases with increasing depth. |
| 3. | is independent of the mass of the earth. |
| 4. | is independent of the mass of the body. |
Subtopic: Acceleration due to Gravity |
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NEET - 2022
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If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:
| 1. | \(\dfrac{\pi RG}{12g}\) | 2. | \(\dfrac{3\pi R}{4gG}\) |
| 3. | \(\dfrac{3g}{4\pi RG}\) | 4. | \(\dfrac{4\pi G}{3gR}\) |
Subtopic: Acceleration due to Gravity |
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NEET - 2023
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A mass falls from a height \(h\) and its time of fall \(t\) is recorded in terms of time period \(T\) of a simple pendulum. On the surface of the earth, it is found that \(t=2T\). The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as \(t'\) and \(T'\). Then we can say:
1. \(t' = \sqrt{2}T\)
2. \(t'>2T'\)
3. \(t'<2T'\)
4. \(t' = 2T'\)
Subtopic: Acceleration due to Gravity |
From NCERT
NEET - 2019
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Acceleration due to gravity is:
| 1. | independent of the mass of the earth. |
| 2. | independent of the mass of the body. |
| 3. | independent of both the mass of the earth and the body. |
| 4. | dependent on both the mass of the earth and the body. |
Subtopic: Acceleration due to Gravity |
78%
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