IGNOU BPHCT-131 June 2022 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) For any two vectors p’ and q, show that

(b) Classify the following ODE on the basis of order, degree, linearity/non-linearity and homogeneity/non-homogeneity : L ai +Ri=E

(c) In the following cases identify the inertial and non-inertial frames, giving reasons : (@ Aball being swung in a circle Gi) A car moving in a straight line at constant speed

(d) Calculate the impulse for a ball of mass 20 g which strikes a wall straight with a speed of 10 ms“! and rebounds at the same speed.

(e) The average angular acceleration of a stone lodged in a rotating car wheel is 100 rad s~?.

Q2.What will be its final angular speed after 3-0 s if it starts from rest ?

(f) Determine the reduced mass of a two body system consisting of a star of mass M and a black hole of mass 150 M.

(g) Write the differential equation for the motion of a one-dimensional spring-mass system. What is its frequency of oscillation in terms of the force constant of the spring and the mass ?

(h) Are water waves transverse or longitudinal ? Explain your answer.

Q3.Answer any two parts: 2x5=10

(a) Determine the torque about the point (0, 1, -1) due to a force F = 1+ 81 —2k acting at the point (2, — 1, — 4). 5

(b) Solve the following boundary value problem: 5 1l6y” +y=0, y

(0)=2, y(2n)=-3

(c) A curve is represented by the following parametric equations : x=4, y=t?4+6, 2=3-2t Determine the unit tangent vector to the curve att =1.

Q4.Answer any two parts: 2x5=10

(a) Acrate is moved across the floor by pulling a rope tied to it. The force on the crate is of magnitude 400 N and is directed at an angle of 60° to the horizontal. The force of kinetic friction on the crate is 100 N and the mass of the crate is 200 kg. Draw the free body diagram and calculate the acceleration of the crate. Also calculate the work done by each force in displacing the crate by 3-0 m. Take g=10 ms”. 14242

(b) State the law of conservation of energy. A block of mass 1-5 kg is pushed against a spring kept on a table and compresses it by 20 cm. Then the block is released and it slides along the table. If the coefficient of kinetic friction between the block and the table is 0-2 and the spring constant is 150 Nm~!, how far will the block move before it comes to rest ? Take g = 10 ms~”. 1+4

(c) Two particles of mass 2m and 5m, respectively, are separated by a distance 2r. A mass m is kept at the mid-point of the line joining them. Determine the net gravitational force on the mass m. At what point on the line should the mass m be kept so that the net gravitational force on it is zero ?

Q5.Answer any two parts: 2x5=10

(a) A disc having rotational inertia 15x10 kgm? is attached to an electric motor which delivers a torque of 30 Nm on the disc. Calculate the disc’s angular speed, angular momentum and work done by the torque in 20s given that it starts from rest. I+1+1+2 BPHCT-131 4

(b) What are the constants of motion for motion under central conservative forces ? Derive the Law of Equal Areas for central force motion. 243

(c) Derive the expression for the total kinetic energy of a two-particle system in terms of the velocity of its c.m. and the velocities of the particles with respect to the c.m.

Q6.Answer any two parts : 2x5=10

(a) The velocities of an object executing SHM are 10 cms and 20 cms! when its displacements are 8cm and 4cm, respectively. Calculate the amplitude of the SHM and its time period. 342

(b) Consider two collinear harmonic oscillations each having frequency , amplitudes a and b, and phases >, and 4,. Determine the amplitude of the motion resulting from the superposition of these two oscillations for @ 6, — bp = 2ma, and

(ii) 6, — o = (2m + 1) 2 where m is an integer. 5

(c) The differential equation of an oscillator of mass 0:2 kg is: a 10% 4 15x =0 dt? dt Calculate the force constant, angular frequency, damping constant and damping factor. What is the nature of damping ? 1x5=5 BPHCT-131 6

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(0)=2, y(2nx)=-3 x=4, y=t?+6, 2=3-2t BPHCT-131 10 4४ 10% 4 15x =0 dt? dt