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Q. No.The height in terms of radius of the earth \((R)\), at which the acceleration due to gravity becomes \(\dfrac{g}{9},\) where \(g\) is acceleration due to gravity on earth's surface, is:
1. \(\sqrt{3}{R}\)
2. \({2}\sqrt{2}{R}\)
3. \(2R\)
4. \(\dfrac{4}{9}R\)
1. \(\sqrt{3}{R}\)
2. \({2}\sqrt{2}{R}\)
3. \(2R\)
4. \(\dfrac{4}{9}R\)
Subtopic: Acceleration due to Gravity |
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If a body of mass \(1~\text{kg}\) falls on the earth from infinity, it attains velocity \((v)\) and kinetic energy \((k)\) on reaching the surface of earth. The values of \(v\) and \(k\) respectively are:
(Take radius of earth to be \(6400~\text{km}\) and \(g = 9.8 ~\text{m/s}^2\))
1. \(11.2 ~\text{km/s} ;~ 6.27 \times 10^7 ~\text{J} \)
2. \(11.2 ~\text{km/s} ; 12.54 \times 10^7 ~\text{J} \)
3. \(8.8 ~\text{km/s} ; 6.27 \times 10^7 ~\text{J} \)
4. \(8.8 ~\text{km/s} ; 12.54 \times 10^7 ~\text{J}\)
(Take radius of earth to be \(6400~\text{km}\) and \(g = 9.8 ~\text{m/s}^2\))
1. \(11.2 ~\text{km/s} ;~ 6.27 \times 10^7 ~\text{J} \)
2. \(11.2 ~\text{km/s} ; 12.54 \times 10^7 ~\text{J} \)
3. \(8.8 ~\text{km/s} ; 6.27 \times 10^7 ~\text{J} \)
4. \(8.8 ~\text{km/s} ; 12.54 \times 10^7 ~\text{J}\)
Subtopic: Escape velocity |
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A planet \((P_1)\) is having around the star of mass \(2M\) in the orbit of radius \(R\). Another planet \((P_2)\) is moving around another star of mass \(4M\) in a orbit of radius \(2R\). Ratio of the time periods of revolution of \(P_1\) and \(P_2\) is:
1. \(\dfrac{1}{2}\)
2. \(2\)
3. \(4\)
4. \(\dfrac{1}{4}\)
1. \(\dfrac{1}{2}\)
2. \(2\)
3. \(4\)
4. \(\dfrac{1}{4}\)
Subtopic: Kepler's Laws |
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When one moves from a point \(16~\text{km}\) below the earth's surface to a point \(16~\text{km}\) above the earth's surface. The change in \(g\) is approximately \(\alpha \% \). The value of \(\alpha\) is:
1. \(0.12\)
2. \(0.25\)
3. \(0.50\)
4. \(0.75\)
1. \(0.12\)
2. \(0.25\)
3. \(0.50\)
4. \(0.75\)
Subtopic: Acceleration due to Gravity |
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A body of mass \(m\) is taken from the surface of earth to a height equal to twice the radius of earth \(\left(R_e\right).\) The increase in potential energy will be:
(\(g\) is acceleration due to gravity at the surface of earth)
1. \(\dfrac{1}{2} m g R_e\)
2. \(\dfrac{3}{4} m g R_e\)
3. \(\dfrac{1}{4} m g R_e\)
4. \(\dfrac{2}{3} m g R_e\)
(\(g\) is acceleration due to gravity at the surface of earth)
1. \(\dfrac{1}{2} m g R_e\)
2. \(\dfrac{3}{4} m g R_e\)
3. \(\dfrac{1}{4} m g R_e\)
4. \(\dfrac{2}{3} m g R_e\)
Subtopic: Gravitational Potential Energy |
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Initially a satellite of \(100~\text{kg}\) is in a circular orbit of radius \(1.5R_E\). This satellite can be moved to a circular orbit of radius \(3R_E\) by supplying \(\alpha \times 10^{6}~\text{J}\) of energy. The value of \(\alpha\) is:
(Take Radius of Earth \(R_E = 6\times 10^{6}~\text{m}\) and \(g = 10~\text{m/s}^2\))
1. \(150\)
2. \(500\)
3. \(100\)
4. \(1000\)
(Take Radius of Earth \(R_E = 6\times 10^{6}~\text{m}\) and \(g = 10~\text{m/s}^2\))
1. \(150\)
2. \(500\)
3. \(100\)
4. \(1000\)
Subtopic: Satellite |
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The escape velocity from a spherical planet \(A\) is \(10~\text{km/s.}\) The escape velocity from another planet \(B\) whose density and radius are \(10\%\) of those of planet \(A\), is:
1. \(1000\) m/s
2. \(200\sqrt{5}\) m/s
3. \(100\sqrt{10}\) m/s
4. \(1000\sqrt{2}\)m/s
1. \(1000\) m/s
2. \(200\sqrt{5}\) m/s
3. \(100\sqrt{10}\) m/s
4. \(1000\sqrt{2}\)m/s
Subtopic: Escape velocity |
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Net gravitational force at the centre of a square is found to be \(F_1\) when four particles having mass \(M,2M,3M\) and \(4M\) are placed at the four corners of the square as shown in the figure and it is \(F_2\) when the positions of \(3M\) and \(4M\) are interchanged. The ratio\(\dfrac{F_1}{F_2}\) is \(\dfrac{\alpha}{\sqrt{5}} .\) The value of \(\alpha\) is:
1. \(2\)
2. \(3\)
3. \(1\)
4. \(2\sqrt{5}\)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(2\sqrt{5}\)
Subtopic: Newton's Law of Gravitation |
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Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Statement I: | A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. |
| Statement II: | The time period of revolution of the satellite is \(T=2 \pi\sqrt{\dfrac{R_e}{g}}\) (for satellite very close to the earth surface), where \(R_e\) radius of earth and \(g\) acceleration due to gravity. |
| 1. | Both Statement I and Statement II are False |
| 2. | Both Statement I and Statement II are True |
| 3. | Statement I is True but Statement II is False |
| 4. | Statement I is False but Statement II is True |
Subtopic: Satellite |
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An object is kept at rest at a distance of \(3R \) above the earth's surface where \(R \) is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume \(M =\) mass of earth, \(G =\) Universal gravitational constant)
1. \(\sqrt{\dfrac{G M}{2 R}}\)
2. \(\sqrt{\dfrac{3 G M}{R}}\)
3. \(\sqrt{\dfrac{2 G M}{R}}\)
4. \(\sqrt{\dfrac{G M}{R}}\)
1. \(\sqrt{\dfrac{G M}{2 R}}\)
2. \(\sqrt{\dfrac{3 G M}{R}}\)
3. \(\sqrt{\dfrac{2 G M}{R}}\)
4. \(\sqrt{\dfrac{G M}{R}}\)
Subtopic: Escape velocity |
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