The gravitational potential energy of an isolated system of three particles, each of mass \(\mathrm{m}\) placed at three corners of an equilateral triangle of side \(\mathrm{l}\) is:
1. | \(-Gm \over \mathrm{l}^2\) | 2. | \(-Gm^2 \over 2\mathrm{l}\) |
3. | \(-2Gm^2 \over \mathrm{l}\) | 4. | \(-3Gm^2 \over \mathrm{l}\) |
Two satellites S1 and S2 are revolving around a planet in coplanar and concentric circular orbits of radii R1 and R2 in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S1 is equal to 104 km. Find the relative speed when they are closest to each other.
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A body of mass m is situated at a distance 4 above the Earth's surface, where is the radius of the Earth. What minimum energy should be given to the body so that it may escape?
1. | mgRe | 2. | 2mgRe |
3. | mgRe/5 | 4. | mgRe/16 |
The potential energy of a satellite having mass m and rotating at a height of 6.4 × m from the Earth's surface is:
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Two particles of mass \(\mathrm{m}\) and \(\mathrm{4m}\) are separated by a distance \(\mathrm{r}.\) Their neutral point is at:
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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)
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Three identical point masses, each of mass 1 kg lie at three points (0, 0), (0, 0.2 m), (0.2 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. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
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:
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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?
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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. | \({3 \over 5 }R\) |