First Year/ First Semester
Subject: Physics I FM: 60
Time: 3 hours PM: 24
Candidates are required to give their answers in their own words
as far as practicable. The figures in the margin indicate full marks.
Year: 2067
Section A
Long Answer Questions
Answer
any four:
1.
A reference frame
rotates with respect to another inertial reference frame with uniform angular velocity w. The position, velocity and acceleration of a
particle in the inertial frame of reference
is 
and 
. Find the acceleration of the particle in the rotating frame of reference.
and . Find the acceleration of the particle in the rotating frame of reference.
2. Consider a system with potential energy 
a) Show that force acting
on the system is given by 
.
.
b) For the system
above it
is given that is translationally invariant i.e.
is translationally invariant i.e.
. Show that linear momentum of the system is conserved.
(3.5 +3.5)
3. a)
State the assumptions made in deducing Stoke’s law for the motion of a small sphere in a viscous medium. Use dimensional
arguments to derive Stoke’s law.
(3.5)
b) Define dipole moment and derive expression
for electric field of a dipole. (3.5)
4. Discuss and derive the boundary conditions imposed on the field vectors 
and 
at the interface of two dielectric media. (7)
and at the interface of two dielectric media. (7)
5.
Use Maxwell’s
equations to derive wave equation for electric and magnetic field.
(7)
Section B
Short Answer Questions:
Answer any eight:
6.
The initial
position of a particle of mass 100g is 
and its initial
velocity is 
ms-1. A
force 
N acts
upon the particle for 5 sec.
Obtain the final velocity and final position.
and its initial
velocity is ms-1. A
force N acts
upon the particle for 5 sec.
Obtain the final velocity and final position.
7. An electron describes a helix of radius
0.2 m and pitch 0.03 cm in a
magnetic field of 50 gauss(104 gauss = 1 Tesla). Calculate the components of its velocity alloy and Perpendicular to the
field. (4)
8. A satellite of m
is revolving around the earth in a circular orbit
of radius r = R + h, where R is the radius of the earth and h is the height of the satellite above earth’s surface. Calculate the angular
momentum of the satellite about the
center of the earth. (4)
9. An LC circuit
oscillates with a frequency of 200 Hz. The capacitance in the circuit is 10 µF. What is the value of the inductance?
10. Two horizontal capillary tubes A and B are connected
together in series so that a steady stream of
liquid flows through them. A is 0.4 mm in internal radius and 250 cm long while B is 0.3 mm in internal
radius and 40 cm long. The pressure of the fluid is 7.5 cm of Hg above the atmospheric pressure at
the entrance point of A.
At the exit point of B the
pressure is atmospheric (76 cm of Hg).
What is the pressure at the junction of A and B?
11.
The screened coulomb potential 
is very common in a conducting medium.
Calculate the corresponding electric field and
charge density. (4)
is very common in a conducting medium.
Calculate the corresponding electric field and
charge density. (4)
12. A plane slab of material
with dielectric constant K has air on both
sides. The electric field in air is E0 and
it is uniform and perpendicular to the boundaries. Find the field inside the dielectric. (4)
13.
Two identical air
capacitors are connected in series and the combination is maintained at a
constant voltage 50v. A dielectric
sheet of dielectric constant 6 and
thickness equal to the –sixth of the
air gap is now inserted into one of the
capacitors. What is the voltage across that capacitor? (4)
14.
Show that magnetic field energy of a system of currents is
given by
where is 
current density, 
is vector potential and is the volume element. The integrated is
carried over volume.
15.
A capacitor C, a resistor R and a battery of voltage V0 are connected in series with a switch. The switch is closed at time
t =0. Set up the differential equation for charge
of on the capacitor and determine it
as a function of time.
Comments
Post a Comment