physics pass 1st sem 2015 question paper. | Assam University.

physics pass 1st sem 2015 question paper. | Assam University.

PHYSICS 

( Pass ) 

lst  Semester 

Course No. PHSP—1O1 

(-Mahtematical Physics, Mechanics and Genetal 

Properties or Matter, Relativity 

FULL Mwks: 35 

Pass Marks-:12 

The figures in the margin indicnte marts for the questions 

Answer flve questions, tacing one from each Unit 

UNIT—I 

1. (a) what is irrotational field? Show hhat the vector field
A__2:2u +s.;+%ki
is irrotational.
(b) ay i + B +C = , then prove that AXBn.BxCI.CxA.H

(-2.)?
2. (a) Define gradient of a scalar field. rind the value orfr where • xi + + zk.
rb) what is the uniL vector perpendieular to both A and B, where A • a -; + k and
, . +4)-k (1+a)+3-7
0

UNIT—II 

3. (a) Find the inverse of the matrix
2J3r
4
6 7 9
Ib) Show that the matrix
1 7 1
5 9 -1
9 13e-5x
is singular. 4+3—7

4. (a) If A and B be wo.non.singUløt aatrices of the same order, then prove that (AB)’ =B-’K1.s
(b) Shor that eveiy diagonal element of a skew-Hermitian matrix is either zero or n purely imaginary number. 4+3p7r

UNIT—Ill 

5. (a) Derive the formulae for the moments or inertia or a uniform solid sphere (1) about its diameter and rii) ab,ut its tangent.
(b) Assuming the earth to be a sphere or uniiorm density s520 kg / m3 and radius 64o0 km, calculate the noment of inertia about its axis or rotation. 4+3-7i

6. (a) what are Lissajous figures? How will you trace graphically the Lissajous figures, when (1) the periods are equal and the phase aifference is n 4 and riE) the periods are in the ratio 2.: 1 and phase difference is zero?
(b) calculate the displacement to amplitude ratio of an SHM, when kinetic energy is 90% of total energy. (1+4)+2-7e

UNIT—IV 

7. (a) Denine Young’s modulus, Poisson’s ratio and Coefficient of rigidity.
(b) Show that for a homogeneous isotropic medium, y = 2ti (1 + i), where letters have their usual meanings. 3+4n7n

8. (a) Derive an cxpresson for the depression at the loaded end of a rectangular cantilever of negligible weight.
(b) Derive the expression for the excess pressure on a curved liquid surface.

UNIT—V 

9. (a) On the basis or uorentz trans(ormat ion., derive an expression for length contraction.
(b) pCAzod4f l'r$ eegth 15 TXSmVingalUngwla length with ‘h4etnéit nf 06 c. Calculate Its length. as it appears to an observer (Q on the earth and (ii) moving with the rod itself. k • velocity of light in free
space). 3+4-7

10. (a) Establish mathematically the Einstein. masa-enera’ relationship.
(b) nhe kinetic energy of a particle ie three times its rest mass energy. what is its veloaty?