Questions on Paper I

 Vector Portion

Q.No. 1             Show that .

Q.No. 2             State and prove Stoke’s theorem.

Q.No. 3             What do you understand by the divergence of a vector? Give its physical significance.

Q.No. 4             Define and explain the gradient and of a scalar function. Show that Grad S = ∇S.

Q.No. 5             State and prove Guass’ divergence theorem.

Q.No. 6             State Stoke’s theorem and a curl of a vector field. Give mathematical expressions.

Chapter No. 6 Particle Dynamics:

Q.No. 1             What is Rotor? Derive the relation for minimum rotational speed which is required to prevent falling.

Q.No. 2             What is conical pendulum? Derive the relation for its period.

Q.No. 3             Define terminal velocity. Derive expression for the terminal velocity of a body falling through a fluid exerting a drag force as a function of velocity.

Chapter No. 7 Work and Energy:

Q.No. 1             State and prove Work-Energy theorem.

Q.No. 2             Give general proof of work-energy principle in case of non-constant forces in one dimension.

Chapter No. 8 Conservation of Energy:

Q.No. 1             Define conservative and non-conservative forces. Show that the spring force is conservative force.

Q.No. 2             Show that the spring force and force of gravity are conservative forces.

Q.No. 3             Show that the one-dimensional motion of a particle acted on by a spring force is sinusoidal.

Chapter No. 9 System of Particles:

Q.No. 1             Prove that in the absence of an external force on a system of particles, the center of mass of system moves with constant velocity.

Chapter No. 10 Collisions:

Q.No. 1             What are elastic and inelastic collisions? Show that in the absence of external force total momentum of the system remains constant.

Q.No. 2             What are elastic and inelastic collisions? Find the velocities of the two colliding bodies after elastic collision in one dimension.

Chapter No. 12 Rotational Dynamics:

Q.No. 1             Define rotational inertia and determine the rotational inertia of a solid rectangular plate (using integral calculus).

Q.No. 2             State and prove parallel-axis theorem.

Q.No. 3             Define rotational inertia. Find moment of inertia for a disc.

Chapter No. 16 Gravitation:

Q.No. 1             State the three Kepler’s laws of planetary motion. Prove the law of periods.

Q.No. 2             State and prove law of area of planetary motion.

Q.No. 3             State and derive the Kepler’s second and third laws.

Q.No. 4             Define absolute potential energy and derive its relation.

Q.No. 5             Define gravitational potential energy and gravitational potential. Find the expression for gravitational potential energy using integration method.

Q.No. 6             What is an escape velocity? Derive an expression for the escape velocity of a body on the surface of earth.

Chapter No. 18 Fluid Dynamics:

Q.No. 1             State and prove Bernoulli’s equation. (09)

Q.No. 2             Using Bernoulli’s theorem, find the thrust on a rocket.

Chapter No. 21 The Special Theory of Relativity:

Q.No. 1             What are the postulates of special theory of relativity? Derive equation .

Q.No. 2             Give the postulates of the special theory of relativity and deduce the relation between mass and energy for special theory of relativity.

Q.No. 3             Prove that E = mc². Discuss its importance.

Q.No. 4             What is an isolated system? Show that in an isolated system of particles the total relativistic energy remains constant.