Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2025 (2 Apr, Shift 1)

Answer: (a)

1. Take O as origin: A = (10,0), B = (10,10), C = (0,10) cm. Use $\tau_z = xF_y - yF_x$; the pivot force at O has no torque.
2. At A: 10 N down gives $10(-10) = -100$; 10 N right gives 0.
3. At B: 10 N up gives $+100$; 10 N right gives $-10(10) = -100$.
4. At C: 10 N up gives 0; F to the left gives $-10(-F) = +10F$.
5. $10F - 100 = 0 \Rightarrow F = 10$ N, so the answer is (a).