1. The figure represents the total acceleration $a$ of a particle moving clockwise in a circle of radius $2.50 \, \text{m}$ at a certain instant of time. For that instant, what is the speed $v$ of the particle?
(A) $5.70 \, \text{m/s}$
(B) $7.50 \, \text{m/s}$
(C) $6.90 \, \text{m/s}$
(D) $8.20 \, \text{m/s}$
(E) $9.30 \, \text{m/s}$

2. Calculate the average power needed to spin a uniform, solid disk of mass $4.40\mathrm{kg}$ and radius $0.70\mathrm{m}$ from rest to 10.0 rad/s in 2.30 s.(A)9.2W(B)23.4 W (C) 14.0 W (D) 12.0 W (E) 16.4 W

3. Tarzan $(M\mathrm{kg})$ tries to cross a river by swinging from a vine as shown in the figure. The vine is $L$ meter long, and his speed at the bottom of the swing is $V\mathrm{m/s}$. And Tarzan knows that the vine has a breaking strength of $S$ Newton. Find the maximum $V$ that Tarzan would not fall in the river.(A) $[(S - Mg)M / L]^{1 / 2}$ (B) $(SL / M)^{1 / 2}$ (C) $[2(S - Mg)L / M]^{1 / 2}$(D) $(2SL / M)^{1 / 2}$ (E) $[(S - Mg)L / M]^{1 / 2}$

4. A bead slides without friction around a loop-the-loop shown in the figure. The bead is released from a height $h = 3.50R$. How large is the normal force on the bead at the top point A if its mass is $10.0\mathrm{g}$?(A) $0.098\mathrm{N}$ (B) $0.980\mathrm{N}$ (C) $1.960\mathrm{N}$ (D) $0.294\mathrm{N}$ (E) $0.196\mathrm{N}$

5. The sound level at a distance of $2.0\mathrm{m}$ from a source is $120\mathrm{dB}$. At what distance is the sound level $100\mathrm{dB}$? (A) $40\mathrm{m}$ (B) $30\mathrm{m}$ (C) $20\mathrm{m}$ (D) $10\mathrm{m}$ (E) $5\mathrm{m}$.

6. A transverse wave on a string is described by the wave function $y = 0.15 \sin(0.8x - 50t)$, where $x$ and $y$ are in meters and $t$ is in seconds. The mass per unit length of this string is $24.0 \, \text{g/m}$. Determine the power transmitted to the wave.(A) $42.18\mathrm{W}$ (B) $21.09\mathrm{W}$ (C) $63.27\mathrm{W}$ (D) $84.36\mathrm{W}$ (E) $2.11\mathrm{W}$

7. The figure illustrates that a particle of mass m slides without friction inside a hemispherical bowl of radius $R$. If the particle starts from rest with a small displacement from equilibrium, it moves in simple harmonic motion with an oscillating angular frequency $\omega$. Find the corresponding period $T$.(A) $\sqrt{g / R}$ (B) $2\pi \sqrt{g / R}$ (C) $2\pi \sqrt{2R / g}$ (D) $2\pi \sqrt{R / g}$ (E) $2\pi \sqrt{R / 2g}$

8. A large storage tank shown in the figure, open at the top and filled with water, develops a very small hole in its side at a point $y_{1}$ (m) below the water level. The rate of flow from the leak is found to be $W$ (m³/s). Determine the diameter of the hole.(A) $(4W / \pi)^{1 / 2} \times (2gy_{1})^{1 / 4}$ (B) $(4W / \pi)^{1 / 2} \times (2gy_{1})^{-1 / 4}$(C) $(W / \pi)^{1 / 2} \times (2gy_{1})^{-1 / 4}$ (D) $(4W / \pi) \times (2gy_{1})^{-1 / 4}$(E) $(4W / \pi)^{1 / 2} \times (gy_{1})^{-1 / 4}$

9. A particular heat engine has a mechanical power output of $2.50\mathrm{kW}$ and an efficiency of $25.0\%$. The engine expels $8.00\times 10^{3}\mathrm{J}$ of exhaust energy in each cycle. Find the time interval for each cycle.(A) 0.533 s (B) 5.330 s (C) 0.266 s (D) 2.660 s (E) 1.066 s

10. As shown in the figure, A 0.10 mole sample of $\mathrm{H}_{2}$ gas is contained in the left side of the container, which has equal volumes left and right. The right side is evacuated. When the valve is opened, the gas streams into the right side. What is the entropy change of the gas? (hint: $\ln(2) = 0.69314$, $R = 8.314 \, \text{J/mole} \cdot \text{K}$)(A) 5.76 J/K (B) 57.6 J/K (C) 2.88 J/K (D) 0.576 J/K (E) 0.288 J/K

11. When the switch in the circuit is closed at $t = 0$, what is the time constant for the circuit to reach steady state? Each of the three resistors has resistance $R$, and each of the three capacitors has capacitance $C$. The internal resistance of the battery is negligible.(A) RC (B) 9RC (C) RC/9 (D) R/C(E) none of those answers

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