Kepler's third law states that square of the period of revolution (T) of a planet around the sun, is proportional to the third power of average distance r between the sun and planet i.e, T2 =Kr3, here K is constant.
If  the masses of the sun and planet are M and m respectively, them as per Newton's law of gravitation force of attraction between them is 
straight F equals space GMm over straight r squared comma space here space straight G space is space gravitational space constant
The relation between G and K is described as

  • GK =4π2

  • GMK =4π2

  • K=G

  • K=G


B.

GMK =4π2

The gravitational force of attraction between the planet and sun provide the centripetal force

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At what height from the surface of earth the gravitation potential and the value of g are -5.4 x 107 J kg-2 and 6.0 m/s2 respectively? (Take the radius of the earth as 6400 km)

  • 1600 km

  • 1400 km

  • 2000 km

  • 2600 km


D.

2600 km

Gravitational potential at some height h from the surface of the earth is given by,

V =     ... (i)
Acceleration due to gravity at some height h from the earth surface can be given as,


  ... (ii)
From equation (i) and (ii), we get


    ... (iii)

 V = -54 x 107 J kg-2
g' = 6.0 m/s2

Radius of Earth, R = 6400 km


Putting the values in Eqn. (iii), we get

 = R+h
h = (9-6.4)x106 = 2.6 x 106 m

 h = 2600 km
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The value of acceleration due to gravity at a depth of 1600 km is equal to

  • 4.9 ms-2

  • 9.8 ms-2

  • 7.35 ms-2

  • 19.6 ms-2


C.

7.35 ms-2

Given, 

Depth (d) = 1600 km

We know that,

gd = g 1 - dRHere, g = 9.8 m/s2 R = 6400 kmgd = g 1 - 16006400    = 9.8 1 - 14    = 9.8 4 - 14 = 9.8 × 34gd = 7.35 ms-2


If the mass of a body is M on the surface of the Earth, the mass of the same body on the surface of the Moon is

  • 6 M

  • M6

  • zero

  • M


D.

M

As we know that the value of acceleration due to gravity (g) is independent of mass, shape, size etc of the body and depends upon the mass and radius of the Earth.


Variation of acceleration due to gravity (g) with distance x from the centre of the Earth is best represented by (R → Radius of the Earth)


D.

The value of g is maximum at the surface of the Earth and g = 0 at centre of the Earth. If one goes away from the Earth surface, again the value of g decreases. Thus, graph (d) is the correct variation of g.

                  


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