IGNOU BPHCT-131 June 2025 Previous Year Question Paper

Q1.Answer any five parts : 5x2=10

(a) Write down the equation of motion of a damped oscillator.

(b) Explain, what is logarithmic decrement.

(c) State Kepler’s third law.

(d) A person is sitting in a bus at rest. The driver suddenly starts the bus. What happens to the person ?

(e) Determine whether the following ordinary differential equation is exact or not : y"dx + 2xydy =0

(f) Two solutions of the second order differential equation : y"+4y=0 are y,=sin2x and yy =cos2x. Calculate their Wronskian and state whether or not their solutions are linearly independent.

(g) In everyday usage, the terms mass and weight are used _ interchangeably. From the point of view of Physics, is it correct ? If not, state the difference between them.

(h) A grinding stone completes 100 clockwise revolutions in 10 seconds. Calculate the average angular speed of a particle situated on it.

Q2.Answer any two parts: 2x5=10

(a) Using method of separation of variables, solve the ordinary differential equation : It is given that y =2 atx=0.

(b) In an LCR circuit, the variation of charge flowing with time in the circuit is given by : pea +R dq +1-0 Solve this equation to determine q as a function of t.

(c) Determine the torque about the point > A A A (-1, 0, 1) due to a force F=i+4j-k being exerted at the point (4, 1, —2).

Q3.Answer any two parts: 2x5=10

(a) Two mutually perpendicular harmonic oscillations of same frequency but different amplitudes and _ arbitrary phase difference are superposed. Obtain the equation of the resultant motion. 5

(b)

(i) Explain the concept of phase of a wave for a transverse wave propagating on a string. 2 Gi) Show that phase difference between two positions defined by x, and x, on a waveform as a given instant of time is given by: 3 Ab= Zea, —x,) for fixed t.

(c) What do you understand by the relaxation time of a damped harmonic oscillator ? A system is executing damped harmonic oscillations and it is observed that in 20 s, the amplitude of oscillations reduces from 4 cm to 2 cm. Calculate its relaxation time.

Q4.Answer any two parts: 2x5=10

(a) A box of mass 10 kg is pulled up by a rope at a constant velocity on a rough inclined plane which makes an angle of 30° with the horizontal. Determine the coefficient of kinetic friction between the box and the plane’s surface if the tension in the string is 120 N. Take g=10ms’. Draw the free body diagram. 4+1

(b) A stone of mass 0.2 kg is swinging in a vertical circle of radius 0.5 m. The speed of the stone is constant and equal to

Q5.0 ms. Calculate the tension in the string at the top and bottom of the circle. Take g =10ms”. 5

(c) The potential energy function for a body is u (x). What is the force acting on the body ? Determine the force acting on the body for u(x)= ae State the conditions for stable, unstable and neutral equilibrium for a potential u (x). 1+14+3

Q6.Answer any two parts: 2x5=10

(a) A vehicle of mass 1500 kg at rest is hit at the back by another vehicle of mass 2500 kg. The final speeds of both vehicles after the collision are known to be 12 ms?! and 8ms™!, respectively in the same direction. If the collision was head-on and elastic, calculate the speed of the second vehicle before collision. 5

(b)

(i) The mass of Saturn is 95 times the mass of earth. One of the moons of Saturn has an orbital period of

Q7.95 days. Calculate the distance between Saturn and its moon. Take mass of earth as 6x107* kg and G=6.67x10 1"! Nmkg@. 4

(ii) A celestial body moves around the sun in an orbit with e = 0.65. State the nature of the orbit. 1

(c) @ Calculate the reduced mass of carbon monoxide molecule by taking the mass of carbon and oxygen atoms as 12 wu and 16 u, respectively. 3

(ii) State the law of conservation of angular momentum for a_two- particle system. 2 y"dx + 2xydy =0 y"+4y=0 @ de y, =sin2x TW y.=cos2x Fl L £4 +R dq +1-0 dt dt ¢ g=10ms? GI 5 1+1+3 =6x104kg a G=6.67x10" Nm“?kg~ |