BSc Physics SEM II ATKT 2018-19 ATKT Physics I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 Use of non- programmable calculator is allowed
2. Q4 Symbols have their usual meanings unless mentioned
3. Q1 (A) Select the correct option 12 marks
   • i) The minimum number of non co-planar vectors, of unequal magnitudes which can be added so that their resultant is equal to zero, is
   • ii) Which of the vector fields is solenoidal?
   • (a) (b) XI-2y J+
   • iii) NM The differential equation js,
   • iv) InanLCR circuit with a D.C. source, the voltage across the resistance may,
   • (a) Continuously Oscillate
   • (b) Be Constant in time
   • (c) Oscillate initially, with decreasing amplitude
   • (d) Linearly increase with time The periodic two oscillators are T and 5T/4 respectively. Both oscillators starts their, oscillation simultaneously from the mid point of their path of motion When the oscillator having periodic time T completes one oscillation, the phase difference between the two oscillators will be,
   • vi) wire having linear mass density 10 gm/m is passed over two supports separated by a distance of 0.25 m. The wire is kept in tension by suspending a 10 kg mass. The midpoint of the wire passes through a magnetic field provided by magnets a.c. supply having a is passed through the wire. If the wire starts vibrating with its resonant frequency, what is the frequency of a.c
   • (B) Answer in one sentence : 03
   • i) does the gradient of a scalar function represent?
   • ii) . How many linearly independent solutions cana linear second order differential equation have?
   • ii), What is a dispersive medium?
   • (C) Fill in the blanks
   • i) the scalar triple product of three vector is zero then we can say that the three ti) If the characteristic equation for a linear second order homogeneous differential equation, with constant coefficients has two equal roots -.say then the most general solution of the given differential equation will be the form
   • iv) When two mutually perpendicular simple harmonic having the same angular frequency and amplitude but having a phase. difference of are simultaneously superimposed the trajectory of the resulting motion will be a
   • v) Waves given out by a point source of light wavefront
4. Q2 (A) Attempt any one. 8 marks
   • i) Find AX(BXC),if B = 2k,C
   • (B) Attempt any one 08
5. Q1 Find the derivative of in the direction of vector
   • (C) Attempt any one. 04
   • i) The diagonals of a parallelogram are Show that the parallelogram is.a rhombus and find the length of its side
   • (A) Attempt any one. 08
6. Q1 Solve for y(x) given, + = 0
   • ii) for a general linear inhomogeneous first order differential
   • (B) Attempt any one. 08
   • i) Solve the differential
   • ii) >0) Discus the solution for:i)d<K i) d=K ii) d>K
   • (C) Attempt any one. 04
   • ii) Obtain the solution for the harmonic oscillator differential equation
7. Q4 (A) Attempt any one. 8 marks
   • i) Obtain the trajectory of a particle on which two parallel simple harmonic motions having different angular are simultaneously ti) Show that a small disturbance on a string tied between two rigid supports, travels along the string as a wave. Hence deduce the speed of the wave?
   • (B) Attempt any one. 08
   • i) Explain normal modes of vibration of a string
   • ii) Obtain an expression for the group velocity collection of waves traveling in a
   • (C) Attempt any one. 04
   • i) The end of a string at z = 0 is driven harmonically at frequency 10 Hz and with amplitude The velocity of the resulting wave is 5 meter/sec. What is the velocity of a point distance z = 3.25.m, when the velocity at z=0 is zero?
   • ii) Check if the followmg functions are solutions of the wave equation:
   • a) sin? (3t)
8. Q5 Attempt any four 20 marks
9. Q1 Find the angle between, & 2k
   • i) Given O(x,y,z) = find iil) Derive an expression for current L-R circuit connected to a D.C. source
   • iv) if the following differential equation is exact, Vv) What are Lissajous patterns?
   • vi) the. trajectory of particle subjected simultaneously to two mutually perpendicular S.H.M.’s given by,

Read from the scan above, so a character or two may differ. The scan is the original.