IGNOU BPHCT-131 December 2025 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) Determine the angle between any two vectors p and q of non-zero magnitude given that : Ip+ql=lp-ql

(b) State the order and degree of the following differential equation : yovEHy

(c) Astronauts are put in a _ rotating circular chamber to be trained in how to withstand high accelerations. What is the acceleration experienced by an astronaut in a chamber in terms of g if it rotates with a constant angular speed of 2.0 rad s! ? Given that in the chamber astronauts travel in a circle of radius of 10 m.

(d) A lift of mass 3000 kg moves 200 m upward at a constant speed in 25.0 s. At what average rate does the force due to the cable do work on the lift ? Take g=10ms-2.

(e) The rotational kinetic energy of a particle in circular motion is 100 J. It moves once in the circle in 22 s. What is the rotational inertia of the particle ?

(f) Using the law of equal areas, explain why an object would move slower when it is farther away from the centre of force.

(g) The displacement of an object executing simple harmonic motion is given by : x = 0.05cos(4nt + 0.0625)m Determine : G) maximum velocity Gi) maximum acceleration

(h) What is relaxation time for a damped oscillation ?

Q2.Answer any two parts: 2x5=10

(a) The position vector of a particle as a function of time is given by : > A A A r(t) =5cos(4t)i+5sin(4t)j +k Determine its velocity and acceleration. Show that both its speed and the magnitude of its acceleration are constant.

(b) Show that the following ODE is exact and solve it : xy'+2x+y=0

(c) In an LCR circuit, an inductance L, a resistance R and a capacitance C are connected in series. The variation of charge ‘q’ flowing through with time ‘?’ in the circuit is given by the differential equation : pea + raed +2=0 dt? dt c Solve this equation to determine ‘q’ as a function of time ‘?’.

Q3.Answer any two parts: 2x5=10

(a) The mass of an aircraft is 50000 kg. It is flying in a straight line at a constant speed of 1000 km h~!. The weight of the aircraft equals the lift force. The pilot increases the thrust of the engine to 90000 N. Suppose the air resistance force equals the engine thrust in 25 s. What is the increased constant speed of the aircraft at that instant ? What is the increase in its speed ?

(b) Calculate the height of a geosynchronous satellite above the surface of the Earth. Given that : G = 6.67x10-!1Nm?2kg-2 , Mass of Earth My = 6.0 x 1024 kg and Radius of Earth = 6.4x106m.

(c) The mass of a_ two-stage rocket launched in free space is 1000 kg at some instant of time. When 600 kg of fuel of the first stage burns in it, the rocket ejects a stream of gas at a relative velocity of 1500 ms-!. What is the rocket’s velocity after the first stage is ejected ?

Q4.Answer any two parts: 2x5=10

(a)

(i) A bicycle travels 150 m along a circular track of radius 15 m. What is the angular displacement in radians of the bicycle from its starting position ? 2

(i) The Earth orbits the sun in 365.25 days in a nearly circular orbit. What is the average angular speed of a particle on Earth’s surface as it orbits the sun ? Take the direction of Earth’s rotation to be +ve direction of the angular displacement. 3

(b) State the law of conservation of angular momentum. A merry-go-round possessing rotational inertia 5000 kgm? is mounted on a frictionless vertical axle and is initially rotating at an angular speed of 1 revolution per minute. A girl jumps on to the platform in the radial direction. If the rotational speed of the merry-go-round reduces to

Q5.8 r.p.m., calculate the girl’s rotational inertia. 1+4

(c) A billiard ball of mass ‘m’ hits another billiard ball of equal mass at rest in an elastic collision and moves along a straight line at an angle of 0 from its original direction of motion. At what angle with each other do the target ball and the projectile move after collision ?

Q6.Answer any two parts: 2x5=10

(a) The amplitude of vibration of a damped spring mass system decreases from 10 cm to 2.5 cm in 200 s. If this oscillator completes 50 oscillations in this time, compare the periods with and without damping. 5

(b) Two collinear harmonic oscillations are represented by : 5 xy(t)=4 sin{ 200 +Zlem Xg(t) =3 sin(20 nt + em Calculate the amplitude, phase constant and period of resultant oscillation obtained on superposing these two collinear oscillations.

(c) (७) How does a pulse differ from a wave ? 2 Gi) A progressive transverse wave is described by : y(x, t) = 0.01 sin(1256t —63x)m Determine the direction of propagation of the wave and calculate the amplitude, wavelength, frequency and velocity. Ip+ql=Ip—al yeve+ Jy x = 0.05cos(4nt + 0.0625)m +

(0) -500०3(40+597

(40)1 +ई xy'+2x+y=0 L aq +R dq +7-0 dt2 dt c¢ &1

(0) 54 sin{ 200 +Zlem yx, t) = 0.01 sin (1256t —63x)m