解答一下第8题---Here is the extracted content from the image: **Question 8** **Question Stem:** 如图所示, 一轻质刚性杆可在竖直平面内绕固定转轴 O 自由转动, 杆长为 2L。杆的中点 M 处固定一质量为 2m 的小球 a, 另一端 N 处固定一质量为 m 的小球 b。现将杆从水平位置 由静止释放, 忽略空气阻力, 重力加速度为 g。下列说法正确的是 **Diagram Description:** - Type: Schematic diagram of a rigid rod with attached masses. - Elements: - A horizontal line segment with points O, M, N, B labeled from left to right. - Point O is indicated as the pivot. - A mass labeled 'a' with value 2m is located above point M. - A mass labeled 'b' with value m is located above point N. - There are handwritten labels near the segments OM and MN/NB which are difficult to interpret as distances due to the mass labels (e.g., "2m a", "m b"). Based on the text, O is the pivot, M is the midpoint (OM = L), and N is the other end (ON = 2L). - Orientation: The rod is shown in a horizontal orientation, indicating the initial position. **Options:** A. 杆转动至竖直位置时, OM 段杆对小球 a 的作用力大小为 $\frac{25}{3}mg$ B. 杆转动至竖直位置时, OM 段杆对小球 a 的作用力大小为 $\frac{14}{3}mg$ C. 从释放到转动至竖直位置过程中, 杆对小球 a 做的功为 $\frac{2}{3}mgL$ D. 从释放到转动至竖直位置过程中, 杆对小球 a 做的功为 $-\frac{1}{3}mgL$ **Other Relevant Text / Annotations:** - Handwritten notes: - "系统机械能守恒" (System mechanical energy conservation) - "$3mgh = \frac{1}{2}(2m)V_a^2 + \frac{1}{2}m V_b^2$" - "$8gL = 2V_a^2 + V_b^2 = 2V_a^2 + (2V_a)^2 = 6V_a^2$" - "$V_a^2 = \frac{8gL}{6} = \frac{4gL}{3}$" - "$V_b = 2V_a$" - "$2mgL - \frac{4}{3}mgL = \frac{2}{3}mgL$" - Circled 'C' next to Option C. - Crossed out 'A' next to Option A. - Crossed out 'B' next to Option B. - "不是 根杆" (Not a rod) next to the diagram. - $\sqrt{\frac{49}{3}}$ --- **Question 9** **Introductory Text for Section:** 二、多项选择题: 本题包括 4 小题, 每小题 4 分, 共 16 分。在每小题给出的四个选项中, 有多项符合题目要求。全部选对的得 4 分, 选对但不全的得 2 分, 有选错的得 0 分。 **Question Stem:** 9. x 轴上两波源 P、Q 的平衡位置坐标分别为 $x_1 = -10m, x_2 = 10m$, 形成的简谐横波在同种均匀介质中相向传播, 某时刻的波形如图所示。已知波的传播速度为 $2m/s$, 下列说法正确的是 **Diagram Description:** - Type: Waveform plot (y vs x). - X-axis: Labeled 'x/cm'. Scale from -10 to 10 with increments of 2. Points P and Q are labeled at x=-10 and x=10 respectively (text indicates meters, but diagram labels cm, assuming meters based on P and Q coordinates). - Y-axis: Labeled 'y/cm'. Scale from -30 to 30 with increments of 15. - Waveform: Shows the superposition of two transverse waves propagating towards each other from P and Q. - Left wave (from P, propagating right): Starts at x=-10, shows crests around x=-9 and x=-1, a trough around x=-5, and zero crossings at -10, -8, -4, 0 (approximate locations based on graph). - Right wave (from Q, propagating left): Starts at x=10, shows crests around x=9 and x=1, a trough around x=5, and zero crossings at 10, 8, 4, 0 (approximate locations based on graph). - Propagation Direction: Arrow above the left wave points right. Arrow above the right wave points left. - Labels and Annotations: P labeled at x=-10, Q labeled at x=10. Origin O labeled at x=0. Circled points on the x-axis at -8, -4, 0, 4, 8. Numbers 1, 2, 3, 4 labeled on the x-axis between -10 and 0, and 1, 2, 3, 4 between 0 and 10 (possibly marking segments). Handwritten annotation: "起振方向看 刚刚传到的位置" (Look at the starting vibration direction, position just reached). Handwritten calculations/notes: "$x_p - q_p = -2$", "$T_r - T_p$". **Options:** (Options are not fully visible in the image)