1. | \(\dfrac{\pi RG}{12g}\) | 2. | \(\dfrac{3\pi R}{4gG}\) |
3. | \(\dfrac{3g}{4\pi RG}\) | 4. | \(\dfrac{4\pi G}{3gR}\) |
1. | \(180 ~\text{N/kg}\) | 2. | \(0.05 ~\text{N/kg}\) |
3. | \(50 ~\text{N/kg}\) | 4. | \(20 ~\text{N/kg}\) |
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. |
Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:
1. | \((4)^2T\) | 2. | \((4)^{\frac13}T\) |
3. | \(2T\) | 4. | \(8T\) |
1. | \(+\frac K2\) | 2. | \(-\frac{K}{2}\) |
3. | \(-\frac{K}{4}\) | 4. | \(+\frac K4\) |
1. | \({S \over 2},{ \sqrt{3gS} \over 2}\) | 2. | \({S \over 4}, \sqrt{3gS \over 2}\) |
3. | \({S \over 4},{ {3gS} \over 2}\) | 4. | \({S \over 4},{ \sqrt{3gS} \over 3}\) |
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. | \(2v\) |