BSc Physics SEM II 2016 17 2016-17 Physics Paper I R Question Paper - Mumbai University | munotes

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1. Q2 Use of non-programmable calculator is permitted
2. Q1 A Select the correct option i If two SHMs of the same amplitude, time period and at right angles to each other; then the resultant vibration is 12 marks
   • (a) elliptical (b) circular
   • ii. A wire fixed at one end is stretched horizontally and has a weight of 1 kg on the other end after passing it over a pulley. If a segment of 15 cm of standing vibration has a frequency 131.Hz, the mass per unit length of the wire is.,
   • iii. If A ,B A.B =
   • iv. If V.@ at(1,-1,0) The degree of the differential equation + 2 Vi. The order of differential equation = N is Answer in ONE statement 3
   • i. Define group velocity il. What do you mean by an ir-rotational vector? iil. What is exact differential?
   • i. Wave is defined as .disturbance propagated through a particular medium
   • ii. The magnitude of maximum value of displacement on either side from the equilibrium position is called iil. The position vector of point P(3,2,1 )with respect to origin is
   • iv. A differential equation which contains only one variables is called.differential
   • v. differential equation is said to be homogeneous when F(x) =
   • Q.P. Code: 03316
3. Q2 Attempt Any ONE: A, B and Care mutually orthogonal unit vectors where: ii if A ,B , then examine whether Bl = 8 marks
   • A .Also find a vector of magnitude 7 and parallelto | A + B] Attempt Any ONE: 8 i Determine the constant a so that the following vector is solenoidal: ii directional derivative of = — 3x?y?z at 2) inthe direction 2? — + 6k. In what direction will the directional derivative be maximum? Find the magnitude of the maximum C Attempt Any ONE: 4 i Prove using vector method that the diagonals of a rhombus are mutually perpendicular ii If finddiv( A) at(0,-1,1)
4. Q3 Attempt any ONE: that the following differential equation is exact and hence find its solution: 8 marks
   • ii. Discuss second order homogeneous linear ordinary differential equations with constant co efficients with roots of the equation real and distinct Attempt any ONE : 8
   • i. magnet is suspended by a vertical string so that it can rotate only in the horizontal plane, The relation between the small horizontal deflection of the magnet under the action of the earth’s magnetic field is Where Lis the moment of inertia of the magnet about vertical axis, M is the magnetic moment of the magnet and H is the horizontal component of the earth’s magnetic field. Solve the equation and find the time period of the oscillations
   • ii. Discuss the general first order linear differential equation with reference to complementary function and particular integral. Obtain its general solution Attempt any ONE: 4 Solve the equation 2y =0 Solve the equation
   • Q.P. Code: 03316
5. Q4 Attempt any ONE: 8 marks
   • i. Obtain an expression for the resultant motion when two SHMs of the same period and with same centre along the same straight line (two collinear SMHs of same period and act simultaneously on a particle. Give some special cases li. Deduce an expression for the speed of transverse wave along a stretched string Attempt any ONE: 8
   • i. Obtain an expression for the resultant motion particle is subjected simultaneously to two mutually perpendicular SHMs of identical period and having same centre. Give some special cases li. Discuss the general solution of wave equation for one dimensional motion Attempt any ONE: 4 that the general solution of the wave equation, Can be represented by y=fi (x-ct) + (x + ct) li. Standing waves are produced by the superposition of two waves, yi= 10sin — 4x) and Find the amplitude of motion at x = 18
6. Q5 Attempt Any Four : Particle is influenced simultaneously by two collinear SHMs which are given by, 6 sin (ot and sin wt. Find the equation of resultant motion the terms: (a) Amplitude, (b) Phase, (c) Epoch, (d) Frequency, (e) Time period Find the projection of the vector Aon the resultant of vectors B and C where: 20 marks
   • v. the following equation for 0 =-k (@ — where k is constant
   • vi. In an LC circuit derive an expression for the charge on the capacitor. Initially both current & charge are zero

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