50. 媽媽以母乳哺餵雙胞胎，家人特別關心兄妹們的消化情況。下列敘述何者正確？
(A) 阿姨：哥哥出生24小時排出的墨綠色物質，是胎毛混合羊水後的產物，持續5~10日才 會消失
(B) 祖父：哥哥排出的是「胎便」，源自於寶寶還在媽媽子宮時，所吞入的羊水、膽汁及 腸細胞屑
(C) 叔叔：妹妹溢奶是因為腸道蠕動過快，導致食物無法進入小腸
(D) 祖母：妹妹溢奶是因幽門發育未完全，且食道下括約肌較鬆弛

1. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of: (A)\( v\sqrt{\frac{m}{2k}} \) (B)\( \frac{1}{2}mv^2 \) (C)\( \frac{1}{4}mv^2 \) (D)\( \frac{mv^2}{4k} \) (E)\( \frac{1}{4}\sqrt{\frac{mv}{k}} \)

2. A hanged ball moves in a horizontal circle, as shown in the figure below. The length of the string is L, and the gravitational acceleration is g. What is the period of this circular motion? (A)\( 2\pi\sqrt{\frac{L\cos\theta}{g}} \) (B)\( \sqrt{\frac{L\cos\theta}{g}} \) (C)\( \frac{1}{2\pi}\sqrt{\frac{L\cos\theta}{g}} \) (D)\( 2\pi\sqrt{\frac{L}{g}}\cos\theta \) (E)\( \frac{1}{2\pi}\sqrt{\frac{L}{g}}\cos\theta \)

3. An object of mass m is initially at rest on a frictionless horizontal plane. If a constant power P acts on this object for t duration, how far will it travel during this interval? (A)\( \sqrt{\frac{8Pt^3}{9m}} \) (B)\( \sqrt{\frac{Pt^3}{8m}} \) (C)\( \sqrt{\frac{8Pt^3}{9m}} \) (D)\( \sqrt{\frac{Pt^3}{m}} \) (E)\( \sqrt{\frac{5Pt^3}{2m}} \)

4. Where is the center of mass of the thin semicircular ring (mass M)? (A) (0, (B)\( (0,) (C)\( (0,) (D)\( (0,) (E)( π0,)

5. A dumbbell has a massless rod and a rod length of 2a. It is placed next to a solid sphere. What is the force difference (the tidal force) between the two particles? (A)\( \frac{4GMa}{5r^3} \) (B)\( \frac{4GMa}{r^3} \) (C)\( \frac{GMa}{r^3} \) (D)\( \frac{GMm}{r^3} \) (E)\( \frac{4GMma}{r^3} \)

6. A small disk of radius \( R_1 \) is fastened coaxially to a larger disk of radius \( R_2 \). The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force \( \overrightarrow{F} \) as shown in fig. below. The tension in the string pulling the block is: (A)\( \frac{mR_1F}{R_2} \) (B)\( \frac{mR_1R_2F}{I - mR_2^2} \) (C)\( \frac{mR_1R_2F}{I + mR_2^2} \) (D)\( \frac{mR_1R_2F}{I - mR_1R_2} \) (E)\( \frac{mR_1R_2F}{I + mR_1R_2} \)

7. A satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy: (A)\( L_2 ＞ L_1 \) and \( K_2 ＞ K_1 \) (B)\( L_2 ＞ L_1 \) and \( K_2 = K_1 \) (C)\( L_2 = L_1 \) and \( K_2 = K_1 \) (D)\( L_2 ＜ L_1 \) and \( K_2 = K_1 \) (E)\( L_2 = L_1 \) and \( K_2 ＞ K_1 \)

8. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g and a is: (A)\( 2\pi\sqrt{L/g} \) (B)\( 2\pi\sqrt{\frac{L}{g+a}} \) (C)\( 2\pi\sqrt{\frac{L}{g-a}} \) (D)\( 2\pi\sqrt{La} \) (E)\( \frac{1}{2\pi}\sqrt{g/L} \)

9. A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m? (A)139 (B)119 (C)129 (D)109 (E)10

10. Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by \( y = 2\sin(\pi x)\cos(3\pi t) \) where x is in m and t is in s. What is the distance (in m) between the first two antinodes? (A)8 (B)2 (C)4 (D)1 (E)0.5

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