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A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

  • at the instant just before the body hits the earth

  • it remains constant all through

  • at the instant just after the body is projected

  • at the instant just after the body is projected


A.

at the instant just before the body hits the earth

We know

P = F. v = Fv cos θ

so just before hitting θ is zero and both F and v are maximum

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A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 x 106 m above the surface of the earth. if earth 's radius is 6.38 x 106 m and g = 9.8 ms-2 then the orbital speed of the  satellite is 

  • 7.76 kms-1

  • 8.56 kms-1

  • 9.13 kms-1

  • 9.13 kms-1


A.

7.76 kms-1

Given, height of a satellite

h = 0.25 x 106

Earth's radius, Re = 6.38 x 106

For the satellite revolving around the  earth, orbital velocity of the satellite



 

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A boy standing at the t op of a tower of 20 m height drops a stone. Assuming g = 10 ms-2, the velocity with which it hits the ground is 

  • 20 m/s

  • 40 m/s

  • 5 m/s

  • 5 m/s


A.

20 m/s

Given, g = 10 ms-2 and h = 20 m

We have

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A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R.G are gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth is 

  • square root of fraction numerator 2 GM over denominator 2 end fraction end root
  • square root of fraction numerator 2 GM over denominator straight R squared end fraction end root
  • square root of 2 gR squared end root
  • square root of 2 gR squared end root

A.

square root of fraction numerator 2 GM over denominator 2 end fraction end root
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A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth. Then,

  • the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant

  • the total mechanical energy of S varies periodically with time

  • the linear momentum of S remains constant in magnitude

  • the linear momentum of S remains constant in magnitude


D.

the linear momentum of S remains constant in magnitude

As we know that, the force on satellite is an only gravitational force which will always be towards the centre of the earth. Thus, the acceleration is S is always directed towards the centre of the earth

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