Merit List

Merit List
Ananda Chandra College, Jalpaiguri

Calender

Mayonic Calender

University Examination at Raigang Univ. College

Thanks to Raiganj College

for their hospitality during our stay there for the B. Sc(Hons.)

Physics Practical Examination, 2011.

Dr. Dhiraj Kr. Basak

Dr. Ranjan Sharma

Question Paper

B.Sc. Part I:First Paper 2010


F.M.-90 First Paper-2006 Time-4 hrs.
Answer Q1 and ANY 5 at least One from each Group
1. (a) A man and a parachute weighing w falls from rest under gravity. If the resistance of air is
proportional to speed v, find the speed as a function of time. Find also the limiting speed.
(b) The overall percentage of failures in an examination is 20%. If 6 candidates appear in the
examination, what is the probability that at least 5 pass?
(c) Prove the multiplication law of probability ) ( ) ( ) ( B P A P B A P = I
(d) A particle has impressed upon it two S.H.Ms of the same period and amplitude at right angles to each
other: x=A sin2ðt/P and y=A sin2ð(t+ä)/P. Find the path of the particle if (i) ä=0 (ii) ä=P/4 (iii) ä=P/8.
(e) Water (ç=0.010 gm/cm/sec) is escaping from a tank through a horizontal capillary tube 50cm in
length and 0.024 cm in diameter. What is the rate of flow of water from the tank when the level in it is 50
cm above that of the tube? How long will it take for the water level to fall a further 10 cm if the cross
sectional area of the tank is everywhere 100 cm2. 3x5
Group-A (Mathematical Physics)
2. (a) Show that the components of A
r
along and perpendicular to B
r
are 2 2 / ) ( & / ) . ( B B x A x B B B B A
r r r r r r
(b) A fluid of density ñ (x, y, z, t) moves with a velocity õ (x, y, z, t). If there are no source or sink, prove
that ( ) v J where
t
J r r r
ñ
ñ
= =
Ý
Ý
+ Þ 0 .
(c) Show that
! 2
! )! 1 2 ( ) 1 ( ) 0 ( 2 n
n P n
n
n
-
- = . 5+5+5
3. (a) Evaluate ç
c
r d A r r
. around the right angled triangle PQR having vertices P(0,0), Q(2,0), R(2,1) and
right angled at Q, where A
r
= ). 4 3 ( ) 2 ( 2 x y j y x i - + +
r r
(b) Show that the line integral of x j y i F
r r r
+ = around a closed curve in xy plane is twice the area
enclosed by the curve using Stokes’ theorem.
(c) Find the series solution of the equation (1- . 0 ) 1 ( 2 ) 2
2
2 = + + - y l l
dx
dy x
dx
y d x 5+4+6
4.(a) Define Laplace’s transform. Solve the equation x y
dx
dy cos 2 = + using Laplace transform.
(b) Find the eigenvalues and eigenvectors for the matrix A= .
.
.

.
1 4
1 1
© If A is Hermitian & A2=1, show that A is unitary. 6+5+4
Group-B (Mechanics)
5. (a)A rain drop falls from rest at a place where the air resistance is proportional to the velocity v and
is kv. (i) set up the equation of motion. (ii) Derive expression for the velocity of the drop as a function of
time. Draw v-t curve (iii) Show that the terminal velocity of the drop is VT=mg/k
(b) Consider a system of particle moving in a plane which interact with one another through pairwise central
forces. Show by using Newton’s 2nd and 3rd law that the total angular momentum of the system is a constant.
(c) Show that the potential and attraction due to a uniform circular disc at any point on its axis, distant x from
the center, are given by ) cos 1 ( 2 ) ( 2
2
2 2
2 è - + -
r
MG and x r x
r
MG
6 +4+5
6.(a) Consider motion of two mass points m1 and m2. Show that the kinetic energy of the particles in the
center of mass frame is equal to ½ µr2 where is the position vector of the particle s and µ is reduced mass
(b) A particle constrained to move along x-axis is subjected to a force of restitution –kx and a force F
T
t
,
which increases uniformly with time t., Discuss its motion, finding the frequency and the point of equilibrium.
(c) Show that the total mechanical energy of a system of particles under conservative forces is conserved.
7.(a) Derive Kepler’s laws of planetary motion from Newton’s law of gravitation. 4+5+6
(b) A particle moves under a force r k F r r
- = where k is a constant and rr
is position vector.
Prove that the motion takes place in a plane. Show that the path described by the particle is an ellipse if it
starts from t=0, x=a, y=0, vx=0 vy=v. Find its period. 8+7
Group-c (General properties of matter)
8.(a) Define coefficient of viscosity and find its dimension.
(b) Derive an expression for the volume of liquid flowing per sec through a capillary tube of radius a. Obtain
the necessary correction.
© Obtain the relation dimensionally between critical velocity and Reynolds’ number and give their physical
significance.
(d) A glass sphere of radius 0.38 falls through a liquid of density 1.21 gm/cm3 and the coefficient of viscosity
is 14 gm/cm/sec. What is the terminal velocity? Density of glass=2.48 g/cm3. 2+6+3+4
9.(a) Explain what do you mean by phase velocity(v) and group velocity(vg). Establish a relation between
them. Show that vp= ã(gë/2ð).
(b) Define self energy. Obtain the self-energy of the spherical object of mass M.
© Show that the two body problem can be converted to a one-body problem. 6+5+4
Group-D (Sound)
10.(a) What is ultrasonic wave? How would you produce it – discuss.
(b) Give the principle of recording and reproduction of sound.
© The initial displacement of a string fixed at both ends is zero. Suppose an impulse is imparted to the string
so that its velocity is u = a x, from x=0 to x=l/4
= a(l/2-x), from x=l/4 to x= l/2
= 0 from x=l/2 to x=l
Find the nature of harmonics present in the vibration of the string. 5+4+6
11.(a) State & explain Doppler’s effect. A tuning fork of frequency 440 Hz approaches a wall with a velocity
4m/s. What will be the number of beats heard between the direct and the reflected sounds, if the velocity of
sound is 332m/s.
(b) A string of length l is fixed at both ends under a tension T. It is plucked at the point x=a to a height h and
then released from rest. The string executes small transverse vibrations.
(i) Show that P.E. = ) ( 2 / 2 2 a l a l h v - µ , µ = mass/length
(ii) Find the total energy of the nth harmonic of the string.
(iii) Show that the total energy at any instant is equal to the initial P.E. of the string. (4+4)+7

Physics Paper I

Physics Exploration

NORTH BENGAL UNIVERSITY

Least squares fit

Data for drawing graph is shown below:
x =1         2          3           4



y =1.7     2.8      3.2        4.2



y =  a  +  bx
 
Fit the data to this equation and find the expected curve.