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 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 additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R₁ to another of radius R₂(R₂> R₁) is 

• 
• 
• 
• 

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

(1) Centre a gravity (CG) of a body is the point at which the weight of the body acts.
(2) Centre  of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
(3) To evaluate the gravitational field intensity due to anybody can be considered to be concentrated at its CG.
(4) The radius of gyration of anybody rotating about an axis is the length of the perpendicular dropped from the CG of the body to the axis.
Which one of the following pairs of statements is correct?

• (4) and (1)

• (1) and (2)

• (2) and (3)

• (2) and (3)