IGNOU BPHCT-131 December 2023 Previous Year Question Paper

Q1.Answer any five parts : 2 each

(a) Define the terms force and torque.

(b) A batsman hits a cricket ball to a distance of 84 m at an angle of 30° east of north. Write down expressions for the x and y- components of its displacement.

(c) The radioactive decay of a transuranic element is modelled by the equation : ao = -AN(t) Solve it if the number of atoms of the element present initially is No.

(d) Write auxiliary equation corresponding to the ODE: y" + 3y'+2y =0 and obtain its roots.

(e) A steel ball is attached to a string. When it is swung in a circular path in the horizontal plane, the string suddenly breaks near the ball. Show the path taken by the steel ball after the string breaks.

(f) A box lying on ground having coefficient of static friction as 0.35 requires horizontal 65 N force to just start moving. Calculate its mass. Take g = 10 ms2.

(g) The differential equation of an oscillator is given by: 42 d. o* + 20% 4 25x =0 dt? dt Calculate the damping factor and specify the nature of damping.

(h) A progressive wave is described by : y(x, 0) = Asin] 1000 nt — em Calculate its wavelength and frequency.

Q2.Answer any two parts :

(a) Obtain the integrating factor for the following ODE and solve it : 5 dy 1

(b) Using the relation for the derivative of a scalar product, show that for a particle undergoing uniform circular motion : @) the velocity is perpendicular to the position vector at each instant of time. Gi) the acceleration is opposite in direction to the position vector and has a magnitude V2/r. 243

(c) Calculate the height of a geostationary orbit from the surface of the earth. 5 Take G = 6.67 x 107! Nm2kg~, R, = 6.37 x10°m and M, = 5.97 x 1074 kg

Q3.Answer any two parts :

(a) A child weighing 35 kg slides down a ramp having a constant slope of 30°. If the speed of the child increases from 1.5 ms! to

Q4.0 ms as he reaches the bottom of the ramp, calculate the length of the ramp using the work-energy theorem. Take the force of kinetic friction as 75 N and g=10ms2. 5

(b) A lift of mass 4500 kg moves 100 m upwards at a constant speed in 10 s. Calculate the average power required by the lift. Take g = 10 ms. 5

(c) Solve the boundary value problem :

Q5.Answer any two parts :

(a) A merry-go-round has a rotational inertia of 5000 kg m? and is initially rotating at an angular speed of 2 r.p.m. A girl jumps onto the platform in the radial direction and the speed of the merry-go-round reduces to

Q6.5 r.p.m. Calculate the rotational inertia of the girl. 5

(b) A satellite weighing 1000 kg is orbiting the earth in an orbit with semi-major axis 5000 km. Calculate the total mechanical energy of the satellite. Also determine the eccentricity and shape of the orbit if the apogee distance is 7500 km. Take G = 6.67 x 10-1 Nm? kg? and Mz = 5.97 x 1074 kg. 3+1+1

(c) A billiard ball of mass 70 g hits another billiard ball of the same mass at rest. If the collision is assumed to be elastic, calculate the angle between these balls after the collision.

Q7.Answer any two parts :

(a) A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 10 cm. After 2.0 minutes, the amplitude decreases to 4 cm. Calculate the time when the amplitude becomes 2 cm and the value of damping factor for this motion. 3+2

(b) A spring mass system 18 set into longitudinal oscillations. Obtain an expression for its total energy. 5

(c) Two mutually perpendicular harmonic oscillations of the same frequency but different amplitudes and phase difference are superimposed. Obtain an expression for the resultant motion.