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

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 

(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)

The dependence of acceleration due to gravity g on the distance r from the centre of the earth assumed to be a sphere of radius R of uniform density is as shown in figure below



The correct figure is

• (4) 

• (1)

• (2)

• (3)

107.

A body mass 1 kg is thrown upwards with velocity 20 ms^-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction?  (g = 10 ms^-2)

• 20 J

• 30 J

• 40 J

• 40 J

The figure shows elliptical orbit of a planet m about the sun S. The shaded are SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B then,

• t₁ > t₂

• t₁ =4 t₂

• t₁ = 2t₂

• t₁ = 2t₂

A roller coaster is designed such that riders experience " weightlessness" as they go round the top of a hill whose radius of curvature is 20 m.  The speed of the car at the top of the hill is between

• 14 m/s and 15 m/s

• 15m/s and 16 m/s

• 16 m/s and 17 m/s

• 16 m/s and 17 m/s

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at a temperature  t^o C, the power received by a unit surface (normal to the incident rays) at a distance R from the centre of the sun is :