JEE Main 2025 Apr 2 Shift 1, Physics Q13: Law of Rotation And Work-Energy Theorem

Taking moments about the pivot $O$ (anticlockwise positive):

Moment due to $10\text{N}$ at $C$ is zero (its line of action passes through $O$).

Moment due to $10\text{N}$ upward at $B=10\ell$ (anticlockwise).

Moment due to $10\text{N}$ rightward at $B=10\ell$ (clockwise).

Moment due to $10\text{N}$ rightward at $A$ is zero (its line of action passes through $O$).

Moment due to $10\text{N}$ downward at $A=10\ell$ (clockwise).

Moment due to $F$ leftward at $C=F\ell$ (anticlockwise).

For rotational equilibrium,

$F\ell +10\ell -10\ell -10\ell =0$

$\Rightarrow F\ell =10\ell$

$\boxed{F=10\text{N}}$