IGNOU BPHCT-131 December 2020 Previous Year Question Paper

Q1.Answer any five parts : 2 each

(a) A box is being pulled by a rope that makes an angle of 60° with the ground, with a force of 80 N along the rope. Calculate the vertical and horizontal components of the force.

(b) Determine whether the following ODE is exact or not ? y? dx + 2xy dy = 0

(c) While riding a bicycle, a child falls forward and off the bicycle, when the bicycle hits a rock. Explain, why ?

(d) Define conservative force. Give an example.

(e) Explain, why dancers are able to increase their angular speed by pulling in their extended arms, while dancing.

(f) Determine the centre of mass coordinates of a system of two objects of masses 3.0 kg and 15 kg, respectively, kept at a distance of 2.0 m from one another.

(g) State the characteristics of simple harmonic motion.

(h) A wave is represented by : y (x, t) = (5 em) sin[ (20 87)8 + (15cm) x | Determine the velocity of the wave.

Q2.Answer any two parts: 5 each

(a) Determine the work done in moving an object from the point (0, 2.0 m, — 2.0 m) to the point (3.0 m, 4.0 m, — 2.0 m) when a > A A constant force F = (4.0N)i+(3.0)j is exerted on it.

(b) Solve the ODE: y" —4y'+ 8y = 0 subject to the initial conditions

(0) = 1 and

(c) The position vector of a particle as a function of time is given by : > s 4 r(t) = 8cos 3ti + 8sin 3t j Determine its velocity and acceleration. Show that both its speed and the magnitude of its acceleration are constant.

Q3.Answer any two parts :

(a) A box of mass 40 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 surface of the plane. It is given that the tension in the rope is 250 N. Draw the free body diagram. Take g = 10 ms . 441

(b) Determine the height of a geosynchronous satellite above the surface of the earth. Take: G = 6.67 x 107! N-m? kg~? Ry = 6.37 x 10° m Mg = 5.97 x 1074 kg 5

(c) State the law of conservation of energy. A wooden cube is pushed across a rough floor at a constant speed by a horizontal force of 12 N and it moves a distance of 7.0 m. If the thermal energy of the cube increases by 32 J, what is the increase in the thermal energy of the floor ?

Q4.Answer any two parts :

(a) A merry-go-round with a radius of 6.0 m is set rotating from rest in a clockwise direction and attains an angular speed of

Q5.50 rads? in 100 s. What is the magnitude and direction of the torque experienced by a child of mass 30 kg about the centre of the merry-go-round if she is sitting at a distance of 3.0 m from the centre ?

Q6.What is her rotational kinetic energy ? 3+2

(b) State Kepler’s third law of planetary motion. One moon of Jupiter has an orbital period of 1.8 days and is at a distance of

Q7.2 units from the centre of Jupiter. Another moon of Jupiter is at a distance of

Q8.7 units from its centre. Calculate is orbital period. 1+4

(c) A ball A collides head-on with another ball B of equal mass. Assuming that ball B is at rest and their collision is elastic, determine the final velocities of these balls.

Q9.Answer any two parts :

(a) Calculate the average of the kinetic energy and potential energy for simple harmonic motion over one complete cycle of oscillation. Take » = 0. 83+2

(b) A particle is simultaneously acted upon by two collinear harmonic oscillations of same frequency but different amplitudes and different initial phases. Determine the displacement of the resultant oscillation. 5

(c) Define logarithmic decrement and quality factor for a weakly damped oscillating system. The amplitude of vibration of a damped spring-mass system reduces from 20 cm to