Q. No.The value of acceleration due to gravity at a height of \(800~\text{km}\) from the surface of the earth (radius of the earth is \(6400~\text{km}\) and value of acceleration due to gravity on the earth's surface is \(981~\text{cm/s}^2\)) is:
1.
\(775 ~\text{cm/s}^2 \)
2.
\(872 ~\text{cm/s}^2 \)
3.
\(981 ~\text{cm/s}^2 \)
4.
\(\text{zero}\)
A satellite of mass \(m\) revolving around the earth in a circular orbit of radius \(r\) has its angular momentum equal to \(L\) about the centre of the earth. The potential energy of the satellite is:
1. \(- \frac{L^{2}}{2 mr}\)
2. \(- \frac{2L^{2}}{mr^2}\)
3. \(- \frac{3L^{2}}{m^2r^2}\)
4. \(- \frac{L^{2}}{mr^2}\)
If \(R\) represents the orbital radius of a planet and \(T\) its orbital period, which of the following graphs correctly depicts the relationship between \(R\) and \(T\) for a planet revolving around the Sun?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A planet moves around the Sun \(S\) in an elliptical orbit, as shown in the figure. If its distances from the Sun at points \(A\) and \(B\) are \(r_1\) and \(r_2\) respectively, what is the ratio of its linear momentum at \(A\) to that at \(B\)?
| 1. | \(\dfrac{r_1}{r_2}\) | 2. | \(\dfrac{r_{1}^{2}}{r_{2}^{2}}\) |
| 3. | \(\dfrac{r_2}{r_1}\) | 4. | \(\dfrac{r_{2}^{2}}{r_{1}^{2}}\) |
Three identical point masses, each of mass \(1~\text{kg}\) lie at three points \((0,0),\) \((0,0.2~\text{m}),\) \((0.2~\text{m}, 0).\) The net gravitational force on the mass at the origin is:
1. \(6.67\times 10^{-9}(\hat i +\hat j)~\text{N}\)
2. \(1.67\times 10^{-9}(\hat i +\hat j) ~\text{N}\)
3. \(1.67\times 10^{-9}(\hat i -\hat j) ~\text{N}\)
4. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
Two particles of mass \(m\) and \(4m\) are separated by a distance \(r.\) Their neutral point is at:
1. \(\frac{r}{2}~\text{from}~m\)
2. \(\frac{r}{3}~\text{from}~4m\)
3. \(\frac{r}{3}~\text{from}~m\)
4. \(\frac{r}{4}~\text{from}~4m\)
| 1. | \(mgR_e\) | 2. | \(2mgR_e\) |
| 3. | \(\frac{mgR_e}{5}\) | 4. | \(\frac{mgR_e}{16}\) |
Two satellites \(S_1\) and \(S_2\) move in the same direction in coplanar, concentric circular orbits of radii \(R_1\) and \(R_2.\) Their orbital periods are \(1~\text{hr}\) and \(8~\text{hr}\) respectively. If \(R_1=10^4~\text{km},\) what is their relative speed when they are closest to each other?
| 1. | \(2\pi \times 10^4~\text{kmph}\) | 2. | \(\pi \times 10^4~\text{kmph}\) |
| 3. | \(\dfrac{\pi}{2} \times 10^4~\text{kmph}\) | 4. | \(\dfrac{\pi}{3} \times 10^4~\text{kmph}\) |
| 1. | \(-Gm \over {l}^2\) | 2. | \(-Gm^2 \over 2{l}\) |
| 3. | \(-2Gm^2 \over {l}\) | 4. | \(-3Gm^2 \over {l}\) |
A planet is revolving around a massive star in a circular orbit of radius \(R\). If the gravitational force of attraction between the planet and the star is inversely proportional to \(R^3,\) then the time period of revolution \(T\) is proportional to:
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)
© 2026 GoodEd Technologies Pvt. Ltd.