IGNOU BPHCT-131 December 2022 Previous Year Question Paper

Q1.Answer any five parts : 2 each > da “pe

(a) Show that a का 0, if a is a constant vector.

(b) Obtain the general solution of the following first order ODE: where F is a constant.

(c) What are inertial and non-inertial frames of reference ?

(d) Calculate the work done by a variable force F =-ax-—bx?, where a and b are constants, in moving a particle of mass m from point x=x, to x=x, along a straight line.

(e) A merry-go-round makes 3 _ complete revolutions every 9 minutes. What is its angular speed in rad s! ?

(f) State Kepler’s law of equal areas for planetary motion.

(g) Write the differential equation describing the SHM of mass m attached to a spring of force constant k.

(h) Depict graphically the time-variation of displacement of a critically damped system.

Q2.Answer any two parts :

(a)

(i) Determine the projection of a+26 on a, where a=i-2j+38k and > a A A b =-i-j+2hk. 3

(i) Obtain a unit vector perpendicular > A A to both A=51+3) and > A A A B=-i-j+2k. 2

(b) Obtain the general solution of ODE : 5 xy' + 2y = x6

(c) Solve the following boundary value problem :

Q3.Answer any two parts :

(a) A train of mass 9.00 x 10° kg is moving in a straight line at a constant speed of

Q4.0 kmh"!. The brakes, which produce a net backward force of 2.70x10°N, are applied for 25.0 s. What is the new speed of the train ? How far has the train travelled in this time ? 3+2

(b) A stone of mass 0.6 kg is swinging in a vertical circle of radius 1.0 m. The speed of the stone is constant and equal to

Q5.0ms. Calculate the tensions in the string at the top and bottom of the circle. Draw the free-body diagrams. Take g =10ms?. Q+2+1

(c) State work-energy theorem. From what height would an object need to be dropped from rest so that it acquires kinetic energy equal to that it has when travelling at a speed of 24.0 ms"! ? Take g = 10ms~?.

Q6.Answer any two parts :

(a)

(0) A bicycle wheel of radius 3.0 m starts from rest and a particle on its rim moves a distance of 30 m in 20 s. Calculate angular displacement of the particle and its average angular speed in the time interval of 20 s. 2 Gi) By what factor will the angular speed of an object change if its rotational inertia is reduced by half, when the net torque on it is zero ? 3

(b) What is the total mechanical energy of a satellite of mass 1000 kg moving about the Earth in an orbit with a = 6000 km ? Here a is length of semi-major axis. Also determine the eccentricity and shape of the orbit when the apogee distance is 10000 km. 3+1+1 Take : G = 6.67 x 10-1! Nm? kg-2 and Mp = 6.0x 104 kg.

(c) @ Determine the reduced mass of a system of two particles having masses

Q7.0 kg and 2.0 kg, respectively. 2 Gi) In a car accident, a car A (mass 1200 kg) is initially at rest. It is hit at the back by a car B of mass 1800 kg. From the markings of the tyres on the road, determined that after their collision, the speeds of car A and B were 12.0ms! and 8.0ms"!, respectively in the same direction. Assuming that the collision is head-on and elastic, determine the speed of car B before collision.

Q8.Answer any two parts :

(a) @) For what value of displacement do the K. E. and P. E. of a simple harmonic oscillator become equal ? 2 Gi) In a spring-mass system, a 0.3 kg mass is attached to a spring of force constant 20Nm-!. The mass is released from rest at x = 20 mm. Calculate the P. E. and K. E. of the system atx =10 mm. 3

(b) Calculate the amplitude and the period of resultant oscillation obtained on superposing following two collinear oscillations : 5 x,(t) = 2 sin(20 mt + em and x(t) = 5sin [29 mt + 4 cm.

(c) The equation of motion of an oscillating body of mass 0.6 kg is : dt? dt Calculate :

(6) force constant k

(ii) angular frequency ७0

(ii) damping constant y

(iv) damping factor b. Also determine the nature of damping. 5 AGO) _ my, xy' + 2y = x6 (@) 3AM 0.6 kg HI UH Ter fT 1.0m 2+2+1 at 10000 km है। 34141 G = 6.67 x107!! Nm? kg? ak = Mg = 6.0x10% kg Tl तथा ७90) Bsin{ 20 nt + =) em कफ +6 de +4x =0 dt? dt