General Physics Contest 2012

Transcription

1 General Physics Contest May 6, (9:am-:5am), Total of 5 pages. Some useful constants: Gas constant R = 8.34 J/mol K Electron mass m e = kg Electron charge e =.6-9 C Electric constant (permittivity) ε = C /N m Magnetic constant (permeability) μ = 4π -7 T m/a Gravitational constant G = N m /kg Mass of Sun =.99 3 kg Mass of Earth = kg Radius of Earth = m Radius of Sun = m Part I Single Choice ( Questions, 3% for each, Use B pencil, No Deduction, Find the Best Choice):. A sports car traveling on a straight road has an initial velocity of m/s; it gains velocity steadily, and 5 s later its velocity is 5 m/s. The acceleration is (A) 5 m/s (B) 4 m/s (C) 3 m/s (D) m/s (E) m/s.. A baseball is thrown at a velocity of 8 m/s at an angle of 3 above the horizontal. What is the maximum height of the ball? (A) m (B) 7 m (C) 8 m (D) m (E) 4 m. 3. An object of mass m is observed to move in a straight line with velocity given by v=bt -ct, where b and c are positive constants. The expression for the force on the object as a function of time is (A) mbt -mct (B) mbt -mct (C) mbt-mc (D) mbt-mc (E) mbt -.5mct. 4. A stone of mass. kg is tied to a string of length.8 m. If you hold the end of this string in your hand and whirl the stone around a circle at the rate of revolutions per second, what is the tension in the string? Ignore gravity in this problem. (A) N (B) 5 N (C) 3 N (D) 4 N (E) 45 N. 5. A fisherman starts his outboard motor by applying a steady tangential force of N by means of a starter rope. The flywheel has a moment of inertia of.5 kg.m and a diameter of. m. Ignoring the effects of friction and the opposing torque due to the compression of the motor, what is the angular speed of the flywheel after it has turned through half a revolution starting from rest? (A) 35.4 rad/s (B) 5. rad/s (C) 56. rad/s (D) 5.6 rad/s (E) 4.5 rad/s. 6. A meteoroid (a chunk of rock) is initially at rest in interplanetary space at a large distance from the Sun. Under the influence of gravity, the meteoroid begins to fall toward the Sun along a straight radial line. With what speed does it strike the Sun? (A) 88 km/s (B) 3 km/s (C) 483 km/s (D) 68 km/s (E) 7 km/s. 7. Electrons in a TV tube are accelerated essentially from rest to a speed of m/s in the electron gun at the back of the tube. If the electron gun is 8. cm long and if the acceleration in the gun is constant, what force is exerted on each electron? (A) N (B) N (C) N (D) N (E) N. 8. A rotating wheel 8 cm in diameter is decelerating at. rad/s. What should be the initial angular speed if the wheel is to stop after exactly one revolution? (A).8 rad/s (B).9 rad/s (C). rad/s (D).4 rad/s (E).6 rad/s. 9. The moment of inertia of the Earth about an axis through the poles is kg m. What is the spin angular momentum? (A).6 33 kg m /s (B).3 33 kg m /s (C) kg m /s (D) kg m /s (E) kg m /s.

2 . A rocket of mass 4 kg, starting from rest, is acted on by a net force of 5 N for s. What is the final velocity of the rocket? (A) 4 m/s (B) m/s (C) m/s (D) 5 m/s (E) 5 m/s.. The figure shows a rectangular brass plate at in which there is cut a rectangular hole of dimension indicated. If the temperature of the plate is raised to 5 : (A) x will increase and y will decrease (B) x will decrease and y will increase (C) both x and y will increase (D) both x and y will decrease (E) depends on the dimension z.. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. The greatest amount of work is required if the process is: (A) adiabatic (B) isothermal (C) isobaric (D) adiabatic or isothermal (both require the same work; isobaric requires less) (E) isothermal or isobaric (both require the same work; adiabatic requires less). 3. The Principle of Equipartition of Energy states that the energy of a gas is shared equally: (A) among the molecules (B) between kinetic and potential energy (C) between translational and vibrational kinetic energy (D)among the relevant degrees of freedom (E) between heat and work. 4. A heat engine operates between K and K. In each cycle it takes J from the hot reservoir, loses 5 J to the cold reservoir and does 75 J of work. This heat engine violates: (A) both the first and second laws of thermodynamics (B) the first law but not the second law of thermodynamics (C) the second law but not the first law of thermodynamics (D) neither the first law nor the second law of thermodynamics (E) cannot answer without knowing the mechanical equivalent of heat. 5. Choose the INCORRECT statement: (A) Gauss s law holds in a vacuum (B) Gauss s law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface (C) Coulomb s law can be derived from Gauss s law and symmetry (D) Gauss s law applies to a closed surface of any shape (E) according to Gauss s law, if a closed surface encloses no charge, then the electric field must vanish everywhere on the Gaussian surface. 6. A parallel plate capacitor is charged and then disconnected from the source. Using insulating handles, the plates are brought closer together. Therefore: (A) the charge on each plate increased (B) the charge on each plate decreased (C) the potential difference between the plates increased (D) the potential difference between the plates decreased (E) the capacitance decreased. 7. A magnetic field CANNOT: (A) exert a force on a charge (B) accelerate a charge (C) change the momentum of a charge (D) change the kinetic energy of a charge (E) change the velocity of a charge.

3 8. Which graph below correctly gives the magnitude of the B field due to an infinitely long straight current carrying wire as a function or the distance r from the wire? (A) (B) (C) (D) (E) 9. A square loop of wire moves with a constant speed v from a field free region, through a region of uniform B field as shown. Which of the five graphs correctly shows the induced current I in the loop as a function of time t? (A) (B) (C) (D) (E). In the diagram, assume that all the lines of B generated by coil # pass through coil #. Coil # has turns and coil # has 4 turns. Then: (A) the current in coil # will be /4 that in coil # (B) the voltage in coil # will be /4 that in coil # (C) the current will be the same in the two coils (D) the voltage will be the same in the two coils (E) the power supplied to coil # is equal to the power delivered by coil #. 3

4 Part II: Multiple Choice (8 Questions, 5% for each, Use B pencil, With Deduction):. A man and a boy, initially at rest on frictionless ice, push each other apart. After a short time, (A) the man is further from the starting point. (B) the boy is further from the starting point. (C) neither is further from the starting point. (D) the man is moving with a higher speed. (E) the boy is moving with a higher speed.. A spring having force constant 5 N/m is loaded with a mass of kg. Which answers are correct in the followings? (A) The period of vibration is.8 s. (B) The period of vibration is.56 s. (C) If the mass is displaced 3 cm and then released. The velocity with which it passes through the equilibrium position is.5 m/s. (D) If the mass is displaced 3 cm and then released. The velocity with which it passes through the equilibrium position is 5 m/s. (E) If the mass is displaced 3 cm and then released. The velocity with which it passes through the equilibrium position is 5 m/s. 3. A space shuttle is in circular orbit 5 km above earth s surface. Which answers are correct? (A) Its orbital speed is 7.8 km/s. (B) Its orbital speed is 3.9 km/s. (C) Its orbital period is around 536 s. (D) Its orbital period is around 3893 s. (E) Its orbital period is around 946 s. 4. A particle moves as follows as a function of time: X = 3. m cos (. radian/s T + π/3), where distance (X) is measured in meters (m) and time (T) in seconds (s). Which answers are correct in the followings? (A) The amplitude of the simple harmonic motion is 3. m. (B) The amplitude of the simple harmonic motion is 6. m. (C) The angular frequency is. radian/s. (D) The angular frequency is.38 cycle/s. (E) The angular frequency is 6.8 radian/s. 5. One mole of ideal monatomic gas is taken around the reversible cycle of Fig. 5. The isothermals are at 5K and 3K. (R is the gas constant) (A) Q = 5Rln, (B) Q =-3R, (C) Q 3 =-3Rln, (D) the work done in one cycle is Rln, (E) the efficiency of the engine is.4. Fig. 5 4

5 6. In A. J. Dempster s mass spectrometer (Fig. 6), two isotopes with masses m and m are accelerated from rest by a potential difference V. They then enter a uniform field B normal to the magnetic field lines. (Assume both isotopes have the same charge q) (A) Both kinetic energies of the accelerated particles are qv (B) The speed of isotope with m is v = qv / m (C) The radius of the path in the magnetic field for the isotope with Fig. 6 m is r m V qb = / (D) r r = m m, (E) r r = m m 7. A cylindrical capacitor consists of a central conductor of radius a surrounded by a cylindrical shell of radius b, as shown in Fig. 7. We assume that the cable is long enough for us to neglect end effects and the linear charge on the central conductor is λ C/m. k = 4πε ) ( (A) The electric field in the region a<r<b is E r =kλ/r (B) The electric field in the region a<r<b is E r =kλ/r (C) The potential difference between the conductors is kλln(b/a) (D) The potential difference between the conductors is kλ(b/a) (E) The capacitance of a length L assuming that air is between the plates: C = πε L ln( b / a) Fig.7 8. A toroidal coil is tightly wound with N turns and carries a current I. We assume that it has a rectangular cross section, as shown in Fig.8. NI a (A) The magnetic field strength within the toroid is B = πr b NI (B) The magnetic field strength within the toroid is B = πr N I (C) The total energy within the toroid is U = 4π h b ln a N h a (D) The self-inductance of the toroid is L = π b N h b (E) The self-inductance of the toroid is L = ln π a Fig. 8 5