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Gravitation

270590 A planet moves around the sun. At a given point \(P\), it is closest from the sun at a distance \(d_{1}\), and has a speed \(V_{1}\). At another point \(\mathbf{Q}\), when it is farthest from the sun at a distance \(d_{2}\), its speed will be

1 \(\frac{d_{1}^{2} V_{1}}{d_{2}}\)
2 \(\frac{d_{2} V_{1}}{d_{1}}\)
3 \(\frac{d_{1} V_{1}}{d_{2}}\)
4 \(\frac{d_{2}^{2} V_{1}}{d_{1}^{2}}\)
Gravitation

270591 If a graph is plotted between \(T^{2}\) and \(r^{3}\) for a planet then, its slope will be

1 \(1 \times 10^{22} \mathrm{~m}^{2}\)
2 \(3 \times 10^{22} \mathrm{~m}^{2}\)
3 \(5 \times 10^{22} \mathrm{~m}^{2}\)
4 \(7 \times 10^{22} \mathrm{~m}^{2}\)
Gravitation

270625 Two satellites \(S_{1}\) and \(S_{2}\) are revolving round 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 \(1 \mathrm{hr}\) and \(8 \mathrm{hr}\). The radius of the orbit of satellite \(S_{1}\) is equal to \(10^{4} \mathbf{~ k m}\). Their relative speed when they are closest, in \(\mathrm{kmph}\) is :

1 \(\frac{\pi}{2} \times 10^{4}\)
2 \(\pi \times 10^{4}\)
3 \(2 \pi \times 10^{4}\)
4 \(4 \pi \times 10^{4}\)
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Gravitation

270590 A planet moves around the sun. At a given point \(P\), it is closest from the sun at a distance \(d_{1}\), and has a speed \(V_{1}\). At another point \(\mathbf{Q}\), when it is farthest from the sun at a distance \(d_{2}\), its speed will be

1 \(\frac{d_{1}^{2} V_{1}}{d_{2}}\)
2 \(\frac{d_{2} V_{1}}{d_{1}}\)
3 \(\frac{d_{1} V_{1}}{d_{2}}\)
4 \(\frac{d_{2}^{2} V_{1}}{d_{1}^{2}}\)
Gravitation

270591 If a graph is plotted between \(T^{2}\) and \(r^{3}\) for a planet then, its slope will be

1 \(1 \times 10^{22} \mathrm{~m}^{2}\)
2 \(3 \times 10^{22} \mathrm{~m}^{2}\)
3 \(5 \times 10^{22} \mathrm{~m}^{2}\)
4 \(7 \times 10^{22} \mathrm{~m}^{2}\)
Gravitation

270625 Two satellites \(S_{1}\) and \(S_{2}\) are revolving round 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 \(1 \mathrm{hr}\) and \(8 \mathrm{hr}\). The radius of the orbit of satellite \(S_{1}\) is equal to \(10^{4} \mathbf{~ k m}\). Their relative speed when they are closest, in \(\mathrm{kmph}\) is :

1 \(\frac{\pi}{2} \times 10^{4}\)
2 \(\pi \times 10^{4}\)
3 \(2 \pi \times 10^{4}\)
4 \(4 \pi \times 10^{4}\)
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Gravitation

270590 A planet moves around the sun. At a given point \(P\), it is closest from the sun at a distance \(d_{1}\), and has a speed \(V_{1}\). At another point \(\mathbf{Q}\), when it is farthest from the sun at a distance \(d_{2}\), its speed will be

1 \(\frac{d_{1}^{2} V_{1}}{d_{2}}\)
2 \(\frac{d_{2} V_{1}}{d_{1}}\)
3 \(\frac{d_{1} V_{1}}{d_{2}}\)
4 \(\frac{d_{2}^{2} V_{1}}{d_{1}^{2}}\)
Gravitation

270591 If a graph is plotted between \(T^{2}\) and \(r^{3}\) for a planet then, its slope will be

1 \(1 \times 10^{22} \mathrm{~m}^{2}\)
2 \(3 \times 10^{22} \mathrm{~m}^{2}\)
3 \(5 \times 10^{22} \mathrm{~m}^{2}\)
4 \(7 \times 10^{22} \mathrm{~m}^{2}\)
Gravitation

270625 Two satellites \(S_{1}\) and \(S_{2}\) are revolving round 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 \(1 \mathrm{hr}\) and \(8 \mathrm{hr}\). The radius of the orbit of satellite \(S_{1}\) is equal to \(10^{4} \mathbf{~ k m}\). Their relative speed when they are closest, in \(\mathrm{kmph}\) is :

1 \(\frac{\pi}{2} \times 10^{4}\)
2 \(\pi \times 10^{4}\)
3 \(2 \pi \times 10^{4}\)
4 \(4 \pi \times 10^{4}\)
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