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. \(R\)
When a planet revolves around the sun in an elliptical orbit, then which of the following remains constant?
1. | Velocity | 2. | Angular velocity |
3. | Areal velocity | 4. | Both 2 & 3 |
1. | \(-0.5\) MJ | 2. | \(-25\) MJ |
3. | \(-5\) MJ | 4. | \(-2.5\) MJ |
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 the speed of an artificial satellite revolving around the earth in a circular orbit be \(2 \over 3\) of the escape velocity from the surface of earth then its altitude above the surface of the earth is
1. | \({4 \over 5 }R\) | 2. | \({2 \over 5 }R\) |
3. | \({1 \over 8 }R\) | 4. | \({3 \over 5 }R\) |
If \(R\) is the radius of the orbit of a planet and \(T\) is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?
1. | 2. | ||
3. | 4. |
The figure shows a planet in an elliptical orbit around the sun (\(S\)). The ratio of the momentum of the planet at point \(A\) to that at point \(B\) is:
1. \(\frac{r_1}{r_2}\)
2. \(\frac{r_{1}^{2}}{r_{2}^{2}}\)
3. \(\frac{r_2}{r_1}\)
4. \(\frac{r_{2}^{2}}{r_{1}^{2}}\)
Three identical point masses, each of mass \(1\) 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. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
A satellite is revolving around the earth with speed \(v_0\). If it is stopped suddenly, then with what velocity will the satellite hit the ground? (\(v_e\)= escape velocity from the earth's surface)
1. \(\sqrt{v_{e}^{2} - v_{0}^{2}}\)
2. \(\sqrt{v_{e}^{2}-2 v_{0}^{2}}\)
3. \(\sqrt{v_{e}^{2}-3 v_{0}^{2}}\)
4. \(\sqrt{v_{e}^{2}-\frac{v_{0}^{2}}{2}}\)