Aligarh Muslim University (AMU) 2009 B.Sc Physics Classical mechanics
I
4293
2008-2009
B.Sc.(HONS.) (PART-III) EXAMINATION (PHYSICS)
CLASSICAL MECHANICS & SPL. RELATIVITY (PH-308)
Maximum Marks: 40 Duration : Three Hours.
Answer the following questions. _ecj
Notations / symbols wherever not explainhave their usual meanings.
Use of calculator is permitted.
1 .(a) Derive the Lagranges equations of motion for a conservation system using
D Alemberts principle. 05
(b) The position vectors of particles 1 and 2 of equal masses vary with time t as
A A
r i = i ( a + v t) and 7 2 = j (b + vt), where a and b are constants. Determine the velocity of their centre-of-mass. Find the relative velocity of particle 1 with respect to particle 2 and the magnitude of the relative velocity. 02
OR
1 (a) State and prove the conservation theorem for the total angular momentum of a
system of particles. 03
(b) What is a conservative force? Show that a conservative force F can be expressed as F = -V V, where V is a scalar function of position coordinates. Write the potential energy function of a system of two charged particles and hence derive a formula for force between the two. 04
-2-
3.(a) Show that the central force motion of two bodies about their centre -of - mass
can be reduced to an equivalent one-body problem. 03
(b) Show that the conservation of angular momentum and the constancy of areal
velocity of radial vector is a general result of any central force motion. 04
n -se
4.(a) Obtain the Hamiltons equations of motion. Using theAequations, obtain the
equation of motion of a linear harmonic oscillator. 03
(b) Discuss the elastic scattering of two equal mass particles with the target at rest in the lab system. Describe the scattering in the C.M.S. 03
5.(a) What is meant by tensors of the same type? Write transformation equations for the
component of a tensor or contra-variant rank 2 and covariant rank 1 under the
Lj
change of coordinates. Discuss the contraction of a tensor A k| . 03
i Define the four-velocity and four-force vectors of a particle and find the value
of their scalar product. 02
V? Vv>
Calculate the kinetic energy (in MeV) and momentum (in MeV / c) of an electron
moving with speed _ . 02
OR
5(a) A particle a of rest mass m a and kinetic energy K a collides with a particle b of rest mass m b and kinetic energy zero. Find a formula for energy in the ('.M.S. 02
Define threshold energy of a reaction and obtain its formula. Calculate the
/
threshold kinetic energy of the incident particle for the following reaction:
ptp->p + p + 7l.
Iho Urgcl is rest. Take m p = 938 MeV/ c 2 and mi =135 MeV/ c 2. 03
(I) Dtrlvo U formula for the Lagrangian of a relativistic particle. 02
ft() Mv th trwmformution equations for the components of the electromagnetic {WM V(NM0N*f wiul H between two reference frames having uniform relative WtMliift lltmg U * mx is, 04
(II) Ihii lh* (NJimMon of motion of a charged particle in an electromagnetic field IVHIllM IlfVWlWU Mtwlw Ilio KIUIKC transformation.
"Wl (
::: i. .____ .
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Attachment: |
| Earning: Approval pending. |
