93年 - [無官方正解]93 台灣聯合大學系統_學士班轉學考試A3：普通物理#139176

1 裝水的開口U型管，在其中一管加入密度是750 kg/m³的油，在水及油皆未溢出管外時，形成4公分長的油柱，則兩管水面高度差（公分為單位）最接近下列何值？假設空氣的密度是1.3 kg/m³。(A)4(B)3(C)2(D)1
(E)0

2 兩個質量都是M的雙星繞它們的質量中心旋轉。已知它們的週期T，軌道半徑r及軌道速度v，則M=(A)(B)(C)(D)
(E)以上皆非

3 初速為零的空心球（I= MR²）由高度80公尺的斜坡頂端滾下。坡面上半段為摩擦力係數0.25的平面，下半段為無摩擦力的平面。球在上半段坡面只有滾動沒有滑動。則到達坡底時，球心的速率最接近下面哪個值(m/s)？設g=10 m/s²。(A)54(B)48(C)36(D)21
(E)15

4 簡諧運動(SHM)一個週期中，動能與位能相等的時間點有幾個？(A)1(B)2(C)4(D)8
(E)以上皆非

5 兩端開口的管子產生第一諧波(first harmonics)的頻率為f，當一端開口封閉後產生的第一諧波頻率為(A)2f(B)1.5f(C)f(D)0.5f
(E)以上皆非

6 質量m的粒子在x-y平面上的運動軌跡為(x,y)=(2t²，3t³-1)，則在t=1時(A)粒子的速度y分量為4(B)作用在粒子上的力y分量為18(C)以原點為參考點的角動量大小為2m(D)以(1,-1)為參考點的角動量大小為-3m
(E)以上皆非

7 同重量的A車與B車，A車10秒鐘可從靜止加速到60公里/小時。而B車在相同的加速時間可達120公里/小時，則B車與A車的輸出馬力比為(A)0.25(B)0.5(C)1(D)2
(E)4

8 在量子波動力學中，波函數Ψ(x)的歸一化(normalization)條件為(A)(B)(C)(D)
(E)

9 一靜止的電子，經電壓為100V的電極加速後，具有動能為（Planck's constant h=6.626×10⁻³⁴ J•s）(A)9.11×10⁻⁹ J(B)1.6×10⁻¹⁷ J(C)6.626×10⁻³⁴ J(D)6.626×10⁻³ J
(E)1.6×10² J

10 在光電效應(photoelectric effect)的實驗中，入射光的頻率(x)與截止電壓(y)的關係為(A)(B)(C)(D)
(E)

11 一有限深位能井，在x=0到L間，位能U=0；在x＜0，x＞L，U=U₀。一粒子置於該位能井中，E＜U，且處於基態(ground state)。請問該粒子出現在哪一個位置的機率最高(A)2L(B)0(C)L/2(D)L
(E)-L

12 某一固態物質具有體積膨脹係數(coefficient of volume expansion) β，則線膨脹係數(coefficient of linear expansion) α為：(A)β^1/3(B)3β(C)0.25β(D)β/3
(E)exp(-β)

13 雙原子分子(N₂、H₂)除具有三維的移動自由度外，也具有兩個轉動自由度。則定壓比熱與定體積比熱的比值γ(=Cₚ/Cᵥ)為(A)7/5(B)5/3(C)7/3(D)3/2
(E)5/2

14 A point charge Q=-500 nC and two unknown point charges, q₁ and q₂, are placed as shown. The electric field at the origin O, due to charges Q, q₁ and q₂ is equal to zero. The charge q₁, in nC, is closest to:(A)120(B)-120(C)-210(D)250
(E)210

15 When there is a net static charge present on an isolated perfect conductor(A)the charge will be uniformly distributed over the surface of the conductor.(B)the surface charge density will be greatest where the conductor is flat and smallest where there are sharp points.(C)the electric field inside the conductor needs not be zero if the conductor is hollow.(D)every point throughout the entire conductor will be at zero potential.
(E)every point throughout the entire conductor will be at a constant potential, but not necessarily at zero potential.

16 If the length and diameter of a wire are both doubled, the resistance will be(A)increased fourfold.(B)unchanged.(C)halved.(D)doubled.
(E)None of these are true.

17 If you were to cut a small permanent bar magnet in half,(A)each piece would be a smaller bar magnet.(B)neither piece would be magnetic.(C)one piece would be a magnetic north pole and the other piece would be a south pole.(D)each piece would be a small magnet, but the magnitudes of magnetic field of the north and south poles would not necessarily be equal on a magnet.
(E)None of these statements is true.

18 A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 9.9 A. A uniform external magnetic field of magnitude 1.8 T in the negative x-direction is present. Segment CD is in the x-z plane and forms 19° with the z-axis. The y-component of the magnetic force on segment AB is closest to:(A)zero(B)-5.1 N(C)-1.7 N(D)+5.1 N
(E)+1.7 N

19 In the following figures, which of the phasor diagrams represents a series RLC circuit driven at resonance?(A)(B)(C)(D)
(E)

20 A tank holds a layer of oil, 1.26 m thick, which floats on a layer of syrup that is 0.9 m thick. Both liquids are clear and do not intermix. A ray from the bottom of the tank crosses the oil-syrup interface at a point 0.90 m from the axis. The ray arrives at the oil-air interface, 2.00 m from the axis and at the critical angle. The index of refraction of the syrup is closest to:
(A)1.62(B)1.41(C)1.85(D)2.06
(E)1.29

21 選出正確的敘述(A)波從輕弦入射重弦，則反射波與入射波反向(out of phase)(B)波從重弦入射輕弦，則反射波與入射波同向(in phase)(C)波的振幅加倍，則傳遞的功率增大四倍(D)弦的線密度減半，則傳遞的功率也減半
(E)弦的張力加倍，則傳遞的功率也加倍

22 實際的彈簧並不遵守Hooke's law: Fₓ=-kx，而是類似Fₓ=-kx+ax²-bx³(k,a與b都是大於零的常數)。一端固定的實際彈簧如外力作用在另一端，使此自由端的位移從x=0到x=c，c＞0，外力作功W，則(A)此時彈簧也作功W(B)如彈簧自由端的位移從x=0到x=-c，則彈簧作功-W(C)彈簧自由端的位移在x=c，儲存在彈簧的位能=W(D)彈簧自由端的位移在x=-c時，儲存在彈簧的位能大於W
(E)外力拉長與壓縮彈簧相同距離所作的功相同

23 質量分別為m₁，m₂的物體(m₁＞m₂)，靜止於無摩擦力的表面上，m₁與m₂受同樣的作用力作用相同的一段時間後，如p=動量，K=動能，則(A)p₁＞p₂(B)p₁＜p₂(C)K₁＞K₂(D)K₁=K₂
(E)K₁＜K₂

24 下列何者是波爾的氫原子模型的假設：(A)電子的位置與動量有測不準關係：Δx·Δp≥h(B)電子只能在某些穩定的軌道(stationary state)間移動(C)電子的角動量滿足量子化條件：mrv=nℏ(D)電子的角動量滿足量子化條件：mr²v=nh
(E)在穩定的狀態下具有能量E，原子發出的光子具有頻率f=E/h

25 有關康卜吞(Compton)散射效應下列何者正確？(A)光子本身遵守能量守恆(B)電子本身遵守能量守恆(C)光子與電子的總和動量守恆(D)散射角越大，散射光波長越長
(E)可以用來證明光子的波動特性

26 一質量為m的粒子在簡諧振盪位能井U=mω²x²/2中，如Ae^(-Bx²)為其薛丁格波動方程的一個解。則(A)能量E=hω/4π(B)能量E=hω/8π(C)B=mωπ/h(D)B=3mωπ/h
(E)B=mω/h

27 在雙狹縫干涉實驗中，狹縫距離為1mm，在中央繞射主極大中，可以觀察到7條干涉條紋。則(A)在第一個次極大的繞射中有5條干涉條紋(B)在第一個次極大的繞射中有3條干涉條紋(C)狹縫寬度為0.125 mm(D)狹縫寬度為0.25 mm
(E)波長越長，中央繞射主極大中可看到的干涉條紋越多，因為繞射效應明顯

28 Which of the following are true statements?(A)Electrons are a kind of electromagnetic wave.(B)In vacuum higher frequency electromagnetic waves travel with higher speeds.(C)Some electromagnetic waves have electric charge.(D)Light speeds up when it moves from water into air.
(E)All electromagnetic waves travel at the same speed in vacuum.

29 The capacitance of a capacitor depends on(A)the geometry(B)the potential difference across it(C)the energy stored in it(D)the imbedded dielectric material
(E)the charge on it

30 In the figure, the electric field lines arising from two charges Q₁ and Q₂ are shown. From this figure,
(A)both Q₁ and Q₂ have the same sign(B)the electric field could be zero at P₂(C)the electric field could be zero at P₁(D)|Q₂|=|Q₁|
(E)None of these is true