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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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 × m from the Earth's surface is:
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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 |
Two satellites \(S_1\) and \(S_2\) are revolving around a planet in coplanar and concentric circular orbits of radii \(R_1\) and \(R_2\) in the same direction respectively. Their respective periods of revolution are \(1\) hr and \(8\) hr. The radius of the orbit of satellite \(S_1\) is equal to \(10^4\) km. Find the 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. \(\frac{\pi}{2} \times 10^4~\text{kmph}\)
4. \(\frac{\pi}{3} \times 10^4~\text{kmph}\)
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. | \(-3Gm^2 \over \mathrm{l}\) |
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. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
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. \(\frac{r_{2}^{2}}{r_{1}^{2}}\)
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. | \({3 \over 5 }R\) |