3. The position of a rock (mass 2.5 kg) is given by $\vec{r}=0.020t^{3}\hat{x}+2.2t\hat{y}-0.060t^{2}\hat{z}$ in meter. Find the torque about z-axis at $t=2.0 s$?
(A) $-0.66\hat{x}+0.048\hat{y}-2.64\hat{z} N\cdot m$
(B) $-0.66\hat{x}+0.048\hat{y} N\cdot m$
(C) $0.144\hat{z} N\cdot m$
(D) $-2.64\hat{z} N\cdot m$
(E) None

4. A thin stick with length d and mass m is rotated continuously at a rate of one revolution per minute about the axis through the point at 0.1d from one end. Which statement is correct? (A) The angular momentum is $73\pi md^{2}/9000 kg\cdot m^{2}/s$. (B) The angular momentum is 0. (C) The torque is $\pi md^{2}/30 N\cdot m$. (D) The torque is $2\pi md^{2} N\cdot m$. (E) None

5. Which of the light energies listed below is the greatest? (elementary charge: $1.60\times10^{-19} C$, Plank constant: $6.63\times10^{-34} m^{2}\cdot kg/s$, speed of light: $3.00\times10^{8} m/s$) (A) $3.06\times10^{-19} J$ (B) $6.00\times10^{14} Hz$ (C) 2.76 eV (D) $1.25\times10^{4} cm^{-1}$ (E) 100 nm

6. As shown in Fig.3, a block of density $\rho{B}$ floats in a fluid of density $\rho{w}$ with a submerged depth of h in static equilibrium. The block has height H and face area A. The fluid container is placed upon a scale. If the block is pushed downward by a force F (with its upper face remaining above the fluid surface), which statement correctly describes the change in the scale reading? (A) It increases more than F. (B) It equals to F. (C) It increases but smaller than F. (D) It equals to the buoyant force of the block. (E) It equals to 0. (Figure 3 shows a block floating in a fluid, with a force F pushing down on it. The fluid container is on a scale.)

7. For the system in previous question, if the block is released from a submerged depth between h and H, what is its oscillation frequency? (A) (B) (C) (D) (E) None

8. The coefficient of volume expansion of gasoline is 0.000950 K-1. A person bought 50.0 liters of gasoline at 40℃. What's the volume of this gasoline at 5℃ (A) 47.0 liter (B) 48.3 liter (C) 49.2 liter (D) 51.7 liter (E) None

9. One traveling wave is described as y(x,t)=6cos(2\pi t+5\pi x+\pi/7), the numerical constants are in SI units. Which statement is correct? (A) The traveling direction is(B) The wavelength is 0.4 m and the frequency is 1.0 Hz. (C) The maximum transverse speed of string element is 12\pi m/s. (D) All (E) None

10. 1 mole of an ideal monatomic gas goes from  a to c in Fig.4, where $p_a = 8$ Pa, $p_c = 3$ Pa, $V_a = 2$ m3, and $V_c = 7$ m3. In the path of $a \rightarrow b \rightarrow c$, work $\dot{W}$ is done by the gas, and heat  Q is added to the gas. Which statement is correct? (A) $W = -15 J (B) Q = 22.5 J (C) Internal energy decreases. (D) All (E) None

11. As shown in Fig.5, the top side of a chamber is covered fully by a glass plate (1.2 mm thick) and a copper plate (5 mm thick). The top face area is 20 cm2. The remaining sides of the chamber consist of thermal insulation materials. One 40 watt hot plate is placed in this chamber. In thermal equilibrium at TL= 25 °C, what's the temperature TH? (thermal conductivity: kCu = 401 W/(m·K), kGlass = 0.8 W/(m·K))(A) 35.65 °C (B) 55.25 °C (C) 75.15 °C (D) 95.85 °C (E) 155.05 °C

12. A non-uniform electric field \(\vec{E} = 3x \hat{i} + y \hat{j} + 5\hat{k}\) V/m pierces the cubic Gaussian surface shown in the Fig.6. What's the total charge inside the cube? (A) \(32\varepsilon_0\) C (B) \(16\varepsilon_0\) C (C) 0 (D) \(8\varepsilon_0\) C (E) None

13. There is an electric potential V(x,y,z)=7xy² in volt, and a +0.2 C charged particle moves from 2î+9ĵ+6k̂ to 5î-2ĵ+7k̂. What's the work done by the electric field? (A) -1216 J (B) 1216 J (C) -198.8 J (D) 198.8 J (E) None

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