(14)Helmholtz coils are sometimes used to obtain a nearly uniform magnetic field in situations where a solenoid would be impractical as shown in the right figure. The magnetic field at the center point on the axis, midway between the coils, how about the derivative of B?
(A)B(x) ≈ B₀ + B'(0)x
(B)B(x) ≈ B₀ + B''(0)x²
(C)B(x) ≈ B₀ + B'''(0)x³
(D)B(x) ≈ B₀ + B''''(0)x⁴
(E)B(x) ≈ B₀ + B'''''(0)x⁵

(1)A satellite of mass 270 kg is placed into Earth orbit at a height of 1250 km above the surface. Assuming a circular orbit, how long does the satellite take to complete one orbit? (G = 6.67×10⁻¹¹ N-m²-kg⁻², Earth mass = 5.97×10²⁴ kg, Earth radius = 6.37×10⁶ m) (A)5.919×10³ s (B)6.623×10³ s (C)5.278×10³ s (D)7.392×10³ s (E)8.019×10³ s

(2)A block of mass m is launched up an inclined plane of angle θ = 30° and length L by an ideal spring with constant k as shown in the right figure. The coefficient of kinetic friction for the inclined plane is μ = 1.0. What is the minimum compression length of the spring for the mass m to reach L? (A) (B) (C) (D) (E)

(3)Stretching a non-linear spring requires an amount of Work given by the equation U = 22x² – 9x³, where U is in Joules and x is in meters. How much force is required to hold this spring stretched out 4.0 m from equilibrium position? (A)256 N (B)246 N (C)278 N (D)212 N (E)298 N

(4)A diffraction grating having 7000 lines per centimeter is illuminated normally with red light from a helium-neon gas laser. If its second-order spectral line is at 62.4°, what is the wavelength of the red laser light? (A)650 nm (B)671 nm (C)633 nm (D)648 nm (E)635 nm

(5)A hollow spherical shell of mass M and radius R starts from rest & rolls down without slipping a hill. Its center of mass drops a total distance h. What is the speed of the ball at the bottom of the hill? (A) (B) (C) (D) (E)

(6)A star rotates once every 55 days. It then undergoes a supernova explosion, hurling most of its mass into space. The inner core of the star, whose radius is initially 30 Mm, collapses into a neutron star only 8 km in radius. The rotating neutron star emits regular pulses of radio waves, making it a pulsar. What is the pulse rate (= rotation rate)? (Assume the core to be a uniform sphere & no external torque.) (A)1.39×10⁵ rev/day (B)1.78×10⁵ rev/day (C)2.03×10⁵ rev/day (D)2.28×10⁵ rev/day (E)2.56×10⁵ rev/day

(7)The waves are a cosine curve with crests 18 m apart. A vertical distance 4.8 m from trough to crest, which takes 1.7 s. Please describe the wave. (A)y(x,t) = 4.8cos(0.70x – 3.70t) (B)y(x,t) = 2.4cos(0.35x - 1.85t) (C)y(x,t) = 2.4cos(0.52x – 1.70t) (D)y(x,t) = 4.8cos(0.35x - 1.85t) (E)y(x,t) = 2.4cos(0.28x – 1.32t)

(8)Given average kinetic energy, (K) = (kT), of a molecule in air at room temperature (20°C = 293K), please determine the root-mean-square speed of an O2 molecule with this energy. (k = 1.38×10⁻²³ J/K, 1u = 1.66×10⁻²⁷ kg) (A)511 m/s (B)671 m/s (C)478 m/s (D)823 m/s (E)379 m/s

(9)In each of the following processes, does the entropy of the named system decrease? (A)cells differentiate in a growing embryo, forming different organs (B)an animal dies, its remains gradually decay (C)an earthquake demolishes a building (D)a power plant burns coal & produces electrical energy (E)a balloon inflates

(10)A semicircular loop of radius a carries a positive charge Q distributed uniformly. What is the magnitude of the electric field at the loop's center (point P in the right figure)? (A) (B) (C) (D) (E)

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