Name of the Organisation : HBCSE – Olympiads
Name of the Paper : Indian National Physics Olympiad Question Paper 2014
Year : 2014
Name of the Subject : Physics
Website : http://olympiads.hbcse.tifr.res.in/
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Indian National Physics Olympiad Question Paper
1. A uniform metallic wire is bent in the form of a parabola and is placed on a horizontal non- conducting oor. A vertical uniform magnetic induction B exists in the region containing the parabolic wire.
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A straight conducting rod (shown by thick line in the gure below),starting from rest at the vertex of the parabola at time t = 0, slides along the parabolic wire with its length perpendicular to the axis of symmetry of the parabola as shown in the gure. Take the equation of the parabola to be y = kx2 where k is a constant. Consider that rod always touches wire.
If the rod moves with a constant speed v,
(a) obtain an expression for the induced emf (1) in terms of time t.
(b) Assuming that the rod has resistance per unit length, obtain current (I1) in the rod as a function of time. Assume that the parabolic wire has no resistance.
(c) Obtain the power needed to keep the rod moving with constant speed v.
2. Two blocks of masses m1 =1.0 kg and m2 = 2.0 kg are connected by a massless elastic spring and are at rest on a smooth horizontal surface with the spring at its natural length. A horizontal force of constant magnitude F = 6:0 N is applied to the block m1 for a certain time t in which m1 suers a displacement x1 = 0:1 m and x2 = 0:05 m. Kinetic energyof the system with respect to center of mass is 0.1 J. The force F is then withdrawn.
(a) Calculate t.
(b) Calculate the speed and the kinetic energy of the center of mass after the force is withdrawn.
(c) Calculate the energy stored in the system.
3.(a) Five vibrations of equal amplitudes are superposed rst with all in phase agreement yielding intensity I1 and then with successive phase dierence 30 yielding intensity Calculate I1/I2
(b) The trajectory of a ray in a non homogeneous medium is represented by x = Asin(y=B) [6] where A and B are positive constants. Compute the index of refraction n in the space between the planes x = A and x = ??A, assuming that n depends only on x and has the value n0 at x = 0. Plot n(x) for x 2 [??A;A].
4. It is well known that the temperature of a closed room goes up if the refrigerator is switched on inside it. A refrigerator compartment set to temperature TC is turned on inside a hut in Leh (Ladakh). The atmosphere (outside the hut) can be considered to be a vast reservoir at constant temperature TO. Walls of hut and refrigerator compartment are conducting. The temperature of the refrigerator compartment is maintained at TC with the help of a compressor engine. We explain the working of the refrigerator engine and the heat ow with the help of the associated gure.
(a) State the law of heat conduction for the walls of the hut and the refrigerator compartment.
(b) We dene the dimensionless quantities k = KH=KC; h = TH=TO and c = TC=TO. Express h is terms of c and k.
(c) Calculate stable temperature TH given TO = 280:0 K, TC = 252:0 K and k = 0:90.
(d) Now another identical refrigerator is put inside the hut. TC and TO do not change but TH, the hut temperature will change to T0H . State laws of heat conduction for hut and ne of the two identical refrigerator compartments.
5. Several men of equal mass are standing on a stationary railroad cart such that the combined [8] mass of all men is equal to the mass of the empty cart.
A rumour that a bomb is on the left half of the cart, however, leads to chaos and and consequently these men start jumping o the cart to the right, with equal velocities relative to the cart.
Find approximately the ratio of the speed (vo) that the cart would acquire if all men jump one after the other to the speed (va) that it would acquire if all of them jump simultaneously o the cart. There is no friction between the cart and the ground.