Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

  • 2.5 R

  • 4.5 R

  • 7.5 R 

  • 1.5 R 


C.

7.5 R 

Suppose, the smaller body cover a distance x before collision, then

width=239
Mx = 5M (9R-x) 
Or,
x= 45R- 5x
Or,
x = 45 R = 7.5 R

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A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 x 1024 kg) have to be compressed to be a black hole?

  • 10-9 m

  • 10-6 m

  • 10-2 m

  • 10-2 m


C.

10-2 m

For a black hole, escape speed is more than the speed of light.

Escape velocity is given by,


Approximating the escape velocity to the speed of light, we have

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Which one of the following plots represents the variation of the gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell).


B.

Inside the shell, E =0
and outside the shell, 
Hence, graph (b) shows the exact result.

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If ve is escape velocity and vo is orbital velocity of a satellite for orbit close to the Earth's surface, then these are related by

  • straight nu subscript degree equals square root of 2 straight v subscript straight e
  • straight v subscript straight o space equals straight v subscript straight e
  • straight v subscript straight e space equals square root of 2 straight v subscript straight o end root
  • straight v subscript straight e space equals square root of 2 straight v subscript straight o end root


C.

straight v subscript straight e space equals square root of 2 straight v subscript straight o end root
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Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by,


B.

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