Let the speed of the planet at the perihelion in figure shown below be vP and the Sun-planet distance SP be rP. Relation between rP, vP to the corresponding quantities at the aphelion rA, vA is:

1.   vPrP = vArA

2.   vArP = vPrA

3.   vAvP = rArP

4.   None of these

Subtopic:  Kepler's Laws |
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Let the speed of the planet at the perihelion in figure shown below be vP and the Sun-planet distance SP be rP. Will the planet take equal times to traverse BAC and CPB ?

1.   No

2.   Yes

3.   Depends on mass of planet 

4.   We can't say anything

Subtopic:  Kepler's Laws |
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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 triangleTake AG = BG = CG = 1 m.

1.   Gm2i^+j^

2.   Gm2i^-j^

3.   0

4.   2Gm2i^+j^

Subtopic:  Newton's Law of Gravitation |
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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 |
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Two uniform solid spheres of equal radii R, but mass and 4have a centre to centre separation 6R, as shown in the figure. The two spheres are held fixed. A projectile of mass is projected from the surface of the sphere of mass directly towards the centre of the second sphere. The expression for the minimum speed 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 |
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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 |
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The moon is at a distance of 3.84×105 km from the earth. Its time period of revolution in days is: (Given k=4π2GME=1.33×10-14 d2 km-3)

1.   17.3 days

2.   33.7 days

3.   27.3 days

4.   4 days

Subtopic:  Satellite |
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