IGNOU BPHCT-131 December 2024 Previous Year Question Paper

Q1.Answer any five parts : 5×2=10

(a) Obtain the unit vector in the direction of the force ˆˆF3 ij

(b) A box is being p ulled by a rope that makes an angle of 45° with the ground, with a force of 80 N along the rope. Calculate the vertical and horizontal component s of the force.

(c) State two characteristics of Simple Harmonic Motion (SHM).

(d) What is a conservative force ? Give one example.

(e) A wave is represented as :

Q2.2cm sin 20s 15cmy x t t x Calculate its speed. [ 3 ] BPHCT–131

(f) Show that the following ordinary differential equation is exact : 33 0y x dx x y dy   

(g) A person is sitting in a bus in motion.

Q3.What happens when it suddenly stops ?

Q4.Answer any two parts : 2×5=10

(a) The undamped torsional oscillations of a wheel are governed by the ordinary differential equation : 2I0d k Determine  as a function of time for : k/I = 125 s , and  0d tdt 1s . [ 4 ] BPHCT–131

(b) Show that for uniform circular motion the velocity is perpendicular to the position vector and the acceleration is perpendicular to the velocity at each instant of time. Determine the direction of the acceleration.

(c) A sph ere of mass m is falling freely from rest under gravity in a lake that offers a resistive force proportional to velocity. Establish the equation of motion of the sphere and solve it.

Q5.Answer any two parts : 2×5=10

(a) A train of mass 10 7 kg is moving in a straight line at a constant speed of 90 km 1h . The brakes which produce a net backward force of 3.20 × 106 N, are [ 5 ] BPHCT–131 applied for 20 s. What is the new speed of the train ? How fa r has the train travelled in this time ? 3+2

(b) State the work -energy theorem. A space - ship of mass 4000 kg is travelling in space at a speed of 8000 ms –1. Its speed is reduced by firing rockets in the opposite direction which generate at thrust of 30000 N over a distance of 2000 km. Calculate the final speed of the spaceship. 1+4

(c) A stone of mass 0.2 kg is swung in a vertical circle of radius 1.0 m at a constant speed of 5 ms –1. Calculate the tension in the string at the top and bottom of the circle. Take g = 10 ms–2. 5 [ 6 ]

Q6.Answer any two parts : 2×5=10

(a) The velocities of an object executing simple harmonic motion are 10 cm 1s and 24 cm 1s when its displacements are 12 cm and 5 cm, respectively. Calculate the amplitude and time period of its oscillations. 5

(b) A progressive wave is described by : sin 1400 20 Determine the direction of propagation and calculate the amplitude, wavelength, frequency and velocity in cm 1s . 5

(c) A damped harmonic oscillator has the amplitude of the first oscillation 10 cm. It reduces to 1 cm after 100 oscillations. If [ 7 ] BPHCT–131 the period of oscillations is 4.6 s, calculate the logarithmic decrement and damping factor.

Q7.Answer any two parts : 2×5=10

(a) The moment of inertia of a wheel about its axis of rotation is 5.0 kgm 2. It is initially at rest and then connected to a motor which delivers a constant torque of 25 Nm about its axis. How much wor k has been done by the motor on the whe el after wheel has gone through 6.0 revolutions ? What is the angular speed of the wheel at that time ?

(b) What is an elastic collision ? A ball collides with another ball of same mass which is at rest. If the collision can be regarded as [ 8 ] BPHCT–131 elastic, ob tain expressions for their fin al velocities after the collision. 1+4

(c)

(i) State Kepler’s law s of planetary motion. 3

(ii) The orbital period of a moon of Jupiter is 1.8 days. It is situated a t a distance of 4.2 units from the centre of Jupiter. Calculate the orbital period of another moon of Jupiter which is at a distance of 10.7 units from its centre. 2 [ 9 ] BPHCT–131 2024 -131

(ii)

(iii)

(iv) 5×2=10 ˆˆF3 ij [ 10 ] BPHCT–131 45° 80 N (SHM)