19. A fiber has index of refraction n = 1.15, and its end surface is normal to the direction of its length. Light is incident from the air. What is the maximum incident angle so that the light can have total internal reflection inside the fiber?

(A) sin⁻¹(0.57) ≈ 35°
(B) sin⁻¹(0.66) ≈ 42°
(C) sin⁻¹(0.75) ≈ 49°
(D) sin⁻¹(0.80) ≈ 53°
(E) sin⁻¹(0.91) ≈ 65°

1. What physical quantity is in common when a person throws a ball upward or horizontally with the same initial speed 5 m/s? (A) The positive work done by the gravity (B) The final speed before hitting the ground (C) The amount of time spent before hitting the ground (D) The vertical component of the final linear momentum before hitting the ground (E) The distance it travels before hitting the ground

2. A semi disk of radius R is shown in the right figure. The origin O (0, 0) is located at the top of the disk. Where is the center of mass of the semi disk? (A) (0, -0.28R) (B) (0, -0.38R) (C) (0, -0.48R) (D) (0, -0.51R) (E) (0, -0.58R)

3. If the semi disk is fixed at point O and starts to rotate with small angle θ under gravity, what is the period of the simple harmonic motion (SHM)? (A)(B) (C) (D) (E)

4. The potential energy of a point mass 1 kg at a distance 0.6 m from the center of a solid sphere with the radius 1 m and the mass 2 kg is (G is the gravitational constant) (A) -2.24G J (B) -1.64G J (C) -0.8G J (D) -2.64G J (E) -1.12G J

5. Two blocks are at rest on a frictionless, level table. Both blocks have the same mass m, connected by a spring of negligible mass. The separation distance when the spring is relaxed is L. During a time interval Δt, a constant force F is applied horizontally to the left block, moving it through a distance x₁. The right block moves through a distance x₂. When the force F is removed, what is the total energy of the system associated with vibration relative to its center of mass? (A) (B) (C) (D)(E) It cannot be determined

6. A comet moves in an elongated elliptical orbit around the sun. At perihelion, the comet is 8.75×10⁷ km from the Sun with the speed 5.5×10⁴ m/sec. At aphelion, it is 5.26×10⁹ km from the sun. The period of the orbit is (A) 64 years (B) 68 years (C) 78 years (D) 75 years (E) 52 years

7. A martial-art monk wants to raise a weight of 5 kg hanging at one end of the uniform rod of length L (1 m) and mass 0.5 kg. He applies force using his thumb and index finger as shown. The minimum force he needs to exert is (A) 100.5 kgw (B) 110.5 kgw (C) 120.5 kgw (D) 125.5 kgw (E) 128.3 kgw

8. A continuous triangular wave on a taut string travels in the positive x-direction with speed v. The tension in the string is F, and the linear mass density of the string is μ. At t = 0, the shape of thepulse is given by y(x, 0) =for 2nL< x < (2n+1)L, and y(x, 0) =for (2n+1)L<x<(2n+2)L, where n = 0, ±1, ±2, ±3... The power of the wave is(A) (B)(C) (D) (E) 0

9. 2 moles of helium gas are heated from 0 °C to 100 °C at constant pressure. The work done by the gas to the environment is (ideal gas constant = 8.31 J·K⁻¹·mol⁻¹) (A) 2770 J (B) 4155 J (C) 1335 J (D) 2493 J (E) 1662 J

10. Five moles of an ideal diatomic gas (γ = 1.4) operate in the cycle shown, where Ta = 400 K, Tc = 200 K and Pc = 100 kPa. Process a-b is isothermal. The efficiency of this heat engine is (A) 9.9 % (B) 15.5 % (C) 27.9 % (D) 35.7 % (E) 41.2 %

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