JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Rotational Mechanics

Since the lamina is free to turn about the pivot O, equilibrium needs the net torque about O to vanish; the pivot reaction takes care of the net force. Writing the side as $\ell$, the two upward $10$ N forces along the top edge together with the rightward and downward $10$ N forces at the far corners give a net torque of magnitude $10\ell$ about O, and the unknown force at C must supply the balancing torque $F\ell$. Equating, $F\ell =10\ell$, so $F=10$ N.