Mechanics — DU B.Sc. (Prog.) Physical Science courses pertaining to Electronics Previous Year Question Papers

2. Attempt Four questions in all. a) „Find a vector whose magnitude is same as that of å = 5î + 12j, and it is parallel to j= 8î + 15j. b) Where is the centre of mass for the collection of masses shown below? M 3M c) Is the Force F = (2xy + z')î + x2j + 2xz R conservative? d) Distinguish between polar vectors and axial vectors with examples.. e) Define Moment of Inertia. Give its physical significance. f) A rod 1m long is moving along its length with a velocity 0.6 c. Calculate its length as it appears to an observer on Earth. 2 (a) If position vector is 7 = xi + yi + zk, calculate gradient of -. (3) (b) Solve the following differential equation y"+y'- 4y = 0, y (x=0) = 1 and 3(a) Distinguish between elastic and inelastic collision. Show that in case of inelastic collision kinetic energy is not conserved. (5) (b) A vessel at rest explodes, breaking into three pieces. Two pieces, having equal masses, fly off perpendicular to one another with the same speed of 30 m/sec. The third piece has three times the mass of each other piece. What is the direction and magnitude of its velocity immediately after the explosion? (5) (c) Find the moment of inertia of a thin uniform rod about an axis passing through one end and perpendicular to its length. (5) 4 (a) Derive the differential equation for a damped harmonic oscillator. Obtain its general solution. Explain the physical significance of the overdamped and underdamped cases. (10) (b) Find the equation of motion for simple pendulum and derive it time period. (5) Q5 (a) What are Galilean Transformations? Show that the laws of Conservation of momentum are invariant to Galilean Transformation equations. (5) (b) Derive the expression for the length contraction in relativity. (5) (c) Two space crafts A and B are moving away from earth in the same direction with speed 0.8 c and 0.6 c respectively. Find the velocity of B with respect to A. (5)