PART I: PHYSICS

Section 1 (Maximum Marks: 12)

• This section contains FOUR (04) questions.

• Each question have FOUR options. ONLY ONE of these four options is the correct answer.

• For each question, choose the option corresponding to the correct answer.

• Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +3 If ONLY the correct option is chosen.

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);

Negative Marks : -1 In all other cases.

Consider a spherical gaseous cloud of mass density (r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If (r) is constant in time, the particle number density n(r) = (r)/m is [ G is universal gravitational constant]