Q. No.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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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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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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Earth has a mass that is \(8\) times greater and a radius that is \(2\) times greater than those of a certain planet. If the escape velocity from Earth is \(11.2 ~\text{km/s,}\) what is the escape velocity from the planet?
1. \(2.8~\) \(\text{km/s}~\)
2. \(5.6~\) \(\text{km/s}~\)
3. \(8.4~\) \(\text{km/s}~\)
4. \(11.2 ~\) \(\text{km/s}~\)
1. \(2.8~\) \(\text{km/s}~\)
2. \(5.6~\) \(\text{km/s}~\)
3. \(8.4~\) \(\text{km/s}~\)
4. \(11.2 ~\) \(\text{km/s}~\)
Subtopic: Escape velocity |
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To project a body of mass \(m\) from earth’s surface to infinity, the required kinetic energy is (assume, the radius of earth is \(R_E, g =\) acceleration due to gravity on the surface of earth):
1. \(\mathrm{mgR}_{\mathrm{E}}\)
2. \(1 / 2 \mathrm{mgR}_{\mathrm{E}}\)
3. \(4 \mathrm{mgR}_{\mathrm{E}}\)
4. \(2 \mathrm{mgR}_{\mathrm{E}} \)
1. \(\mathrm{mgR}_{\mathrm{E}}\)
2. \(1 / 2 \mathrm{mgR}_{\mathrm{E}}\)
3. \(4 \mathrm{mgR}_{\mathrm{E}}\)
4. \(2 \mathrm{mgR}_{\mathrm{E}} \)
Subtopic: Escape velocity |
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A planet of mass of \(\frac{1}{6}^\text{th}\) of earth's mass, the radius of \( \frac{1}{3}^\text{rd}\) of earth’s radius. If the escape speed for Earth is \(11.2 ~\text{km/s},\) then the escape speed for the planet shall be: (nearest integer)
1. \(7~\text{km/s}\)
2. \(9~\text{km/s}\)
3. \(11~\text{km/s}\)
4. \(8~\text{km/s}\)
1. \(7~\text{km/s}\)
2. \(9~\text{km/s}\)
3. \(11~\text{km/s}\)
4. \(8~\text{km/s}\)
Subtopic: Escape velocity |
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The mass of the moon is \( \frac{1}{81}\) times the mass of a planet and the radius is \( \frac{1}{9}\) times the radius of the planet. The ratio of escape speed from the planet to escape speed from the moon is:
1. \(2\)
2. \(4\)
3. \(5\)
4. \(3\)
1. \(2\)
2. \(4\)
3. \(5\)
4. \(3\)
Subtopic: Escape velocity |
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A planet is revolving in a circular orbit of radius \(R\) around the sun with speed \(v.\) If another planet is revolving in a circular orbit of radius \(\frac{R}{4},\) then its velocity is:
1. \(2v\)
2. \(4v\)
3. \(6v\)
4. \(8v\)
1. \(2v\)
2. \(4v\)
3. \(6v\)
4. \(8v\)
Subtopic: Escape velocity |
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A satellite is moving around earth surface. How much minimum speed should be increased so that it escapes from earth surface? (\(g\) = acceleration due to gravity, \(R\) = radius of earth)
1. \(2\sqrt{gR} \)
2. \(\left({\sqrt{2}-1}\right)\sqrt{gR} \)
3. \(\dfrac{gR}{2}\)
4. \(\left({\sqrt{3}-1}\right)\sqrt{gR}\)
1. \(2\sqrt{gR} \)
2. \(\left({\sqrt{2}-1}\right)\sqrt{gR} \)
3. \(\dfrac{gR}{2}\)
4. \(\left({\sqrt{3}-1}\right)\sqrt{gR}\)
Subtopic: Escape velocity |
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
In the light of the above statements choose the correct answer from the options given below:
| Assertion (A): | Earth has atmosphere and moon doesn’t. |
| Reason (R): | Escape speed on moon is less than that of earth. |
In the light of the above statements choose the correct answer from the options given below:
| 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. | Both (A) and (R) are false. |
Subtopic: Escape velocity |
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