Let the speed of the planet at the perihelion \(P\) in figure shown below be \(v_{_P}\) and the Sun-planet distance \(\mathrm{SP}\) be \(r_{_P}.\) Relation between \((r_{_P},~v_{_P})\) to the corresponding quantities at the aphelion \((r_{_A},~v_{_A})\) is:

              
1. \(v_{_P} r_{_P} =v_{_A} r_{_A}\)
2. \(v_{_A} r_{_P} =v_{_P} r_{_A}\)
3. \(v_{_A} v_{_P} = r_{_A}r_{_P}\)
4. none of these

Subtopic:  Kepler's Laws |
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​Let the speed of the planet at the perihelion \(P\) in the figure shown below be \(v_p\) and the Sun-planet distance \(SP\) be \(r_p\). Will the planet take equal time to traverse \(BAC\) and \(CPB?\)

   

1. no
2. yes
3. depends on the mass of the planet 
4. we can't say anything

Subtopic:  Kepler's Laws |
 58%
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Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle
(
Take \(AG=BG=CG=1\) m.)

       

1. \(Gm^2(\hat{i}+\hat{j})\)
2. \(Gm^2(\hat{i}-\hat{j})\)
3. zero
4. \(2Gm^2(\hat{i}+\hat{j})\)

Subtopic:  Newton's Law of Gravitation |
 82%
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Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle if the mass at the vertex A is doubled? Take AG = BG = CG = 1 m.

1.   Gm2 i^+j^

2.   Gm2 i^-j^

3.   0

4.   2Gm2 j^

Subtopic:  Newton's Law of Gravitation |
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The potential energy of a system of four particles placed at the vertices of a square of side l (as shown in the figure below) and the potential at the centre of the square, respectively, are:

1.   -5.41Gm2l and 0

2.   0 and -5.41Gm2l 

3.   -5.41Gm2l and -42Gml

4.   0 and 0

Subtopic:  Gravitational Potential Energy |
 58%
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Two uniform solid spheres of equal radii \(\mathrm{R},\) but mass \(\mathrm{M}\) and \(\mathrm{4M}\) have a centre to centre separation \(6\mathrm{R},\) as shown in the figure. The two spheres are held fixed. A projectile of mass \(\mathrm{m}\) is projected from the surface of the sphere of mass \(\mathrm{M}\) directly towards the centre of the second sphere. The expression for the minimum speed \(\mathrm{v}\) of the projectile so that it reaches the surface of the second sphere is:

      

1.   3GM5R1/2

2.   2GM5R1/2

3.   3GM2R1/2

4.   5GM3R1/2

Subtopic:  Gravitational Potential Energy |
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The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of 9.4×103 km. The mass of mars is:
1. 6.48×1023 kg
2. 6.48×1025 kg
3. 6.48×1020 kg
4. 6.48×1021 kg

Subtopic:  Satellite |
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You are given the following data: g 9.81 m/s2, RE = 6.37×106 m, the distance to the moon, R = 3.84×108 m and the time period of the moon’s revolution is 27.3 days. Mass of the Earth ME in two different ways is:

1.   5.97×1024 kg and 6.02×1024 kg

2.   5.97×1024 kg and 6.02×1023 kg

3.   5.97×1023 kg and 6.02×1024 kg

4.   5.97×1023 kg and 6.02×1023 kg

Subtopic:  Satellite |
 55%
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Constant k = 10-13 s2m-3 in days and kilometres is?

1.   10-13 d2km-3

2.   1.33×1014 dkm-3

3.   10-13 d2km

4.   1.33×10-14 d2km-3

Subtopic:  Satellite |
 57%
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The moon is at a distance of \(3.84\times10^5~\text{km}\) from the earth. Its time period of revolution in days is: \((\text{Given }k=\frac{4\pi^2}{GM_E}=1.33\times10^{-14}~\text{days}^{2}-\text{km}^{-3})\)
1. \(17.3\) days
2. \(33.7\) days
3. \(27.3\) days
4. \(4\) days
Subtopic:  Satellite |
 63%
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