Gravitation

An alternating electric field of frequency v is applied across the dees (radius =R ) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it are given by

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2 m, 4 m, 8 m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be

• -G

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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 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 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

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 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 

A particle of mass M is situated at the centre of spherical shell of mass and radius a. Th magnitude of the gravitational potential at a points situated at a/2 distance from the centre, will be

• 2GM/a

• 3GM/a

• 4GM/a

• 4GM/a

The radii of circular orbits of two satellites A and B of the earth are 4R and R, respectively. If the speed of satellite A is 3v. then the speed of satellite B will be

• 3v/4

• 6v

• 12 v

• 12 v

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a.The gravitational potential at a point situated  at a/2 distance  from the centre will be

• -3 GM/ a

• -2 GM/a

• -GM/a

• -GM/a