Q. No.If \(v_e\) is the escape velocity and \(v_0\) is the orbital velocity of a satellite for orbit close to the earth's surface, then these are related by:
1.
\(v_o=v_e\)
2.
\(v_e=\sqrt{2v_o}\)
3.
\(v_e=\sqrt{2}~v_o\)
4.
\(v_o=\sqrt{2}~v_e\)
| 1. | \(g' = 3g\) | 2. | \(g' = 9g\) |
| 3. | \(g' = \frac{g}{9}\) | 4. | \(g' = 27g\) |
Rohini satellite is at a height of \(500\) km and Insat-B is at a height of \(3600\) km from the surface of the earth. The relation between their orbital velocity (\(v_R,~v_i\)) is:
1. \(v_R>v_i\)
2. \(v_R<v_i\)
3. \(v_R=v_i\)
4. no specific relation
Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:
1. \(3F\)
2. \(F\)
3. \(F/3\)
4. \(F/9\)
| 1. | \(\frac{S}{2},\frac{\sqrt{3gS}}{2}\) | 2. | \(\frac{S}{4}, \sqrt{\frac{3gS}{2}}\) |
| 3. | \(\frac{S}{4},\frac{3gS}{2}\) | 4. | \(\frac{S}{4},\frac{\sqrt{3gS}}{3}\) |
The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is:
| 1. | \(3v\) | 2. | \(4v\) |
| 3. | \(v\) | 4. | \(2v\) |
A planet revolving in elliptical orbit has:
| (A) | a constant velocity of revolution. |
| (B) | the least velocity when it is nearest to the sun. |
| (C) | its areal velocity directly proportional to its velocity. |
| (D) | its areal velocity inversely proportional to its velocity. |
| (E) | to follow a trajectory such that the areal velocity is constant. |
Choose the correct answer from the options given below:
| 1. | (A) only | 2. | (D) only |
| 3. | (C) only | 4. | (E) only |
An artificial satellite revolves around a planet for which gravitational force \((F)\) varies with the distance \(r\) from its centre as \(F \propto r^{2}.\) If \(v_0\) is its orbital speed, then:
| 1. | \(v_{0} \propto r^{-1/2}\) | 2. | \(v_{0} \propto r^{3/2}\) |
| 3. | \(v_{0} \propto r^{-3/2}\) | 4. | \(v_{0} \propto r\) |
A comet orbits the sun in a highly elliptical orbit. The comet has a constant:
1. linear speed
2. angular speed
3. angular momentum
4. kinetic energy
Choose the correct alternative.
| 1. | Acceleration due to gravity increases with increasing altitude. |
| 2. | Acceleration due to gravity remains unchanged with increasing altitude. |
| 3. | Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density). |
| 4. | Acceleration due to gravity decreases with increasing depth (assume the earth to be a sphere of uniform density). |
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