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.
