Standard +0.3 This is a straightforward moments problem requiring students to find the center of mass of a composite body and apply equilibrium conditions. While it involves multiple rods and requires careful geometric reasoning about the perpendicular distance, the solution follows a standard method (find combined COM, take moments about a point) with no novel insights needed. Slightly easier than average due to the convenient numbers (weights equal lengths) and clear diagram.
4
\includegraphics[max width=\textwidth, alt={}, center]{b96a99a6-3df4-4000-9bf1-aab7ab954b4a-3_563_707_274_721}
A rigid body \(A B C\) consists of two uniform rods \(A B\) and \(B C\), rigidly joined at \(B\). The lengths of \(A B\) and \(B C\) are 13 cm and 20 cm respectively, and their weights are 13 N and 20 N respectively. The distance of \(B\) from \(A C\) is 12 cm . The body hangs in equilibrium, with \(A C\) horizontal, from two vertical strings attached at \(A\) and \(C\). Find the tension in each string.
Horiz distances of B from A and C are 5 cm and 16 cm. \(21U_A = 13 \times 18.5 + 20 \times 8\). \(T_A + T_C = 33\). Hence \(T_A = 19.1\) N and \(T_C = 13.9\) N
M1, A1, M1, A1, A1, M1, A1, A1 (8 marks)
For appropriate use of Pythagoras; For both distances correct; For any moments equation for the system; For any one relevant term correct; For a completely correct equation; For resolving, or using another moments eqn; For correct answer 19.1; For correct answer 13.9
Horiz distances of B from A and C are 5 cm and 16 cm. $21U_A = 13 \times 18.5 + 20 \times 8$. $T_A + T_C = 33$. Hence $T_A = 19.1$ N and $T_C = 13.9$ N | M1, A1, M1, A1, A1, M1, A1, A1 (8 marks) | For appropriate use of Pythagoras; For both distances correct; For any moments equation for the system; For any one relevant term correct; For a completely correct equation; For resolving, or using another moments eqn; For correct answer 19.1; For correct answer 13.9
---
4\\
\includegraphics[max width=\textwidth, alt={}, center]{b96a99a6-3df4-4000-9bf1-aab7ab954b4a-3_563_707_274_721}
A rigid body $A B C$ consists of two uniform rods $A B$ and $B C$, rigidly joined at $B$. The lengths of $A B$ and $B C$ are 13 cm and 20 cm respectively, and their weights are 13 N and 20 N respectively. The distance of $B$ from $A C$ is 12 cm . The body hangs in equilibrium, with $A C$ horizontal, from two vertical strings attached at $A$ and $C$. Find the tension in each string.
\hfill \mbox{\textit{OCR M2 Q4 [8]}}