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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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. | \(-3Gm^2 \over \mathrm{l}\) |
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 |
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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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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3. | 4. |
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. |
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:
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3. | 4. |
The value of acceleration due to gravity at a height of 800 km from the surface of the earth (radius of the earth is 6400 km and value of acceleration due to gravity on the earth's surface is 981 cm/) is:
1. | \(775 \mathrm{~cm} / \mathrm{s}^2 \) | 2. | \(872 \mathrm{~cm} / \mathrm{s}^2 \) |
3. | \(981 \mathrm{~cm} / \mathrm{s}^2 \) | 4. | \(Zero\) |
A planet moves around the sun. At a point P, it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point Q, when it is farthest from the sun at distance \(d_2,\) its speed will be:
1. | \(d_2v_1 \over d_1\) | 2. | \(d_1v_1 \over d_2\) |
3. | \(d_1^2v_1 \over d_2\) | 4. | \(d_2^2v_1 \over d_1\) |