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. | 2. | ||
3. | 4. |
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 . If it is stopped suddenly, then with what velocity will the satellite hit the ground? ( = escape velocity from the earth's surface)
1.
2.
3.
4.
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. \(\frac{r}{4}~\text{from}~4m\)
The potential energy of a satellite having mass \(m\) and rotating at a height of \(6.4\times 10^{6}~\text{m}\) from the Earth's surface is:
1. \(-0.5mg R_e\)
2. \(-mg R_e\)
3. \(-2mg R_e\)
4. \(4mg R_e\)
1. | \(mgR_e\) | 2. | \(2mgR_e\) |
3. | \(\frac{mgR_e}{5}\) | 4. | \(\frac{mgR_e}{16}\) |
1. | \(775 ~\text{cm/s}^2 \) | 2. | \(872 ~\text{cm/s}^2 \) |
3. | \(981 ~\text{cm/s}^2 \) | 4. | \(\text{zero}\) |