A particle of mass \(m\) is projected with a velocity, \(v=kV_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is: (Where \(V_e=\) escape velocity, \(R=\) radius of the earth)
1. | \(\dfrac{R^{2}k}{1+k}\) | 2. | \(\dfrac{Rk^{2}}{1-k^{2}}\) |
3. | \(R\left ( \dfrac{k}{1-k} \right )^{2}\) | 4. | \(R\left ( \dfrac{k}{1+k} \right )^{2}\) |
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. | \(2v\) |
1. | \({S \over 2},{ \sqrt{3gS} \over 2}\) | 2. | \({S \over 4}, \sqrt{3gS \over 2}\) |
3. | \({S \over 4},{ {3gS} \over 2}\) | 4. | \({S \over 4},{ \sqrt{3gS} \over 3}\) |
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. | \(\frac{2}{9}\) m | 2. | \(18\) m |
3. | \(6\) m | 4. | \(\frac{2}{3}\) m |
With what velocity should a particle be projected so that its height becomes equal to the radius of the earth?
1.
2.
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4.
If a body of mass m placed on the earth's surface is taken to a height of h = 3R, then the change in gravitational potential energy is:
1.
2.
3.
4.
For moon, its mass is \(\frac{1}{81}\) of Earth's mass and its diameter is \(\frac{1}{3.7}\) of Earth's diameter. If acceleration due to gravity at Earth's surface is \(9.8\) m/, then at the moon, its value is:
1. | \(2.86\) m/s2 | 2. | \(1.65\) m/s2 |
3. | \(8.65\) m/s2 | 4. | \(5.16\) m/s2 |
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
If the radius of the earth shrinks by 1%, then for acceleration due to gravity, there would be:
1. No change at the poles
2. No change at the equator
3. Maximum change at the equator
4. Equal change at all locations